diff --git a/CHANGELOG.md b/CHANGELOG.md
index d89c7b09..935d3407 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -11,6 +11,8 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
     by changing `CopyDirectories` to `CopyPaths` - Fixes [Issue #332](https://github.com/dsccommunity/ComputerManagementDsc/issues/332).
   - Pin `Pester` module to 4.10.1 because Pester 5.0 is missing code
     coverage - Fixes [Issue #336](https://github.com/dsccommunity/ComputerManagementDsc/issues/336).
+- ScheduledTask
+  - Add "StopExisting" to valid values for MultipleInstances parameter - Fixes [Issue #333](https://github.com/dsccommunity/ComputerManagementDsc/issues/333).
 
 ## [8.2.0] - 2020-05-05
 
diff --git a/source/DSCResources/DSC_ScheduledTask/DSC_ScheduledTask.psm1 b/source/DSCResources/DSC_ScheduledTask/DSC_ScheduledTask.psm1
index 1ac366e7..79b366ee 100644
--- a/source/DSCResources/DSC_ScheduledTask/DSC_ScheduledTask.psm1
+++ b/source/DSCResources/DSC_ScheduledTask/DSC_ScheduledTask.psm1
@@ -390,7 +390,7 @@ function Set-TargetResource
         $ExecutionTimeLimit = '08:00:00',
 
         [Parameter()]
-        [ValidateSet('IgnoreNew', 'Parallel', 'Queue')]
+        [ValidateSet('IgnoreNew', 'Parallel', 'Queue', 'StopExisting')]
         [System.String]
         $MultipleInstances = 'Queue',
 
@@ -546,12 +546,16 @@ function Set-TargetResource
             WakeToRun                       = $WakeToRun
             RestartOnIdle                   = $RestartOnIdle
             DontStopOnIdleEnd               = $DontStopOnIdleEnd
-            MultipleInstances               = $MultipleInstances
             Priority                        = $Priority
             RestartCount                    = $RestartCount
             RunOnlyIfNetworkAvailable       = $RunOnlyIfNetworkAvailable
         }
 
+        if ($MultipleInstances -ne 'StopExisting')
+        {
+            $settingParameters.Add('MultipleInstances', $MultipleInstances)
+        }
+
         if ($IdleDuration -gt [System.TimeSpan] '00:00:00')
         {
             $settingParameters.Add('IdleDuration', $IdleDuration)
@@ -579,6 +583,16 @@ function Set-TargetResource
 
         $setting = New-ScheduledTaskSettingsSet @settingParameters
 
+    <#  The following workaround is needed because the TASK_INSTANCES_STOP_EXISTING value of
+        https://docs.microsoft.com/en-us/windows/win32/taskschd/tasksettings-multipleinstances is missing
+        from the Microsoft.PowerShell.Cmdletization.GeneratedTypes.ScheduledTask.MultipleInstancesEnum,
+        which is used for the other values of $MultipleInstances. (at least currently, as of June, 2020)
+    #>
+        if ($MultipleInstances -eq 'StopExisting')
+        {
+            $setting.CimInstanceProperties.Item('MultipleInstances').Value = 3
+        }
+
         $scheduledTaskArguments += @{
             Settings = $setting
         }
@@ -1262,7 +1276,7 @@ function Test-TargetResource
         $ExecutionTimeLimit = '08:00:00',
 
         [Parameter()]
-        [ValidateSet('IgnoreNew', 'Parallel', 'Queue')]
+        [ValidateSet('IgnoreNew', 'Parallel', 'Queue', 'StopExisting')]
         [System.String]
         $MultipleInstances = 'Queue',
 
@@ -1810,6 +1824,19 @@ function Get-CurrentResource
             $PrincipalId = 'UserId'
         }
 
+    <#  The following workaround is needed because Get-StartedTask currently returns NULL for the value
+        of $settings.MultipleInstances when the started task is set to "Stop the existing instance".
+        https://windowsserver.uservoice.com/forums/301869-powershell/suggestions/40685125-bug-get-scheduledtask-returns-null-for-value-of-m
+    #>
+        $MultipleInstances = [System.String] $settings.MultipleInstances
+        if ([System.String]::IsNullOrEmpty($MultipleInstances))
+        {
+            if ($task.settings.CimInstanceProperties.Item('MultipleInstances').Value -eq 3)
+            {
+                $MultipleInstances = 'StopExisting'
+            }
+        }
+
         $result = @{
             TaskName                        = $task.TaskName
             TaskPath                        = $task.TaskPath
@@ -1847,7 +1874,7 @@ function Get-CurrentResource
             RestartOnIdle                   = $settings.IdleSettings.RestartOnIdle
             DontStopOnIdleEnd               = -not $settings.IdleSettings.StopOnIdleEnd
             ExecutionTimeLimit              = ConvertTo-TimeSpanStringFromScheduledTaskString -TimeSpan $settings.ExecutionTimeLimit
-            MultipleInstances               = [System.String] $settings.MultipleInstances
+            MultipleInstances               = $MultipleInstances
             Priority                        = $settings.Priority
             RestartCount                    = $settings.RestartCount
             RestartInterval                 = ConvertTo-TimeSpanStringFromScheduledTaskString -TimeSpan $settings.RestartInterval
diff --git a/source/DSCResources/DSC_ScheduledTask/DSC_ScheduledTask.schema.mof b/source/DSCResources/DSC_ScheduledTask/DSC_ScheduledTask.schema.mof
index 6583b6b9..941b833b 100644
--- a/source/DSCResources/DSC_ScheduledTask/DSC_ScheduledTask.schema.mof
+++ b/source/DSCResources/DSC_ScheduledTask/DSC_ScheduledTask.schema.mof
@@ -38,7 +38,7 @@ class DSC_ScheduledTask : OMI_BaseResource
     [Write, Description("Indicates that Task Scheduler restarts the task when the computer cycles into an idle condition more than once.")] Boolean RestartOnIdle;
     [Write, Description("Indicates that Task Scheduler does not terminate the task if the idle condition ends before the task is completed.")] Boolean DontStopOnIdleEnd;
     [Write, Description("Specifies the amount of time that Task Scheduler is allowed to complete the task.")] String ExecutionTimeLimit;
-    [Write, Description("Specifies the policy that defines how Task Scheduler handles multiple instances of the task."), ValueMap{"IgnoreNew","Parallel","Queue"}, Values{"IgnoreNew","Parallel","Queue"}] String MultipleInstances;
+    [Write, Description("Specifies the policy that defines how Task Scheduler handles multiple instances of the task."), ValueMap{"IgnoreNew","Parallel","Queue", "StopExisting"}, Values{"IgnoreNew","Parallel","Queue", "StopExisting"}] String MultipleInstances;
     [Write, Description("Specifies the priority level of the task. Priority must be an integer from 0 (highest priority) to 10 (lowest priority). The default value is 7. Priority levels 7 and 8 are used for background tasks. Priority levels 4, 5, and 6 are used for interactive tasks.")] Uint32 Priority;
     [Write, Description("Specifies the number of times that Task Scheduler attempts to restart the task.")] Uint32 RestartCount;
     [Write, Description("Specifies the amount of time that Task Scheduler attempts to restart the task.")] String RestartInterval;
diff --git a/source/DSCResources/DSC_ScheduledTask/README.md b/source/DSCResources/DSC_ScheduledTask/README.md
index 8ea83832..efc6df41 100644
--- a/source/DSCResources/DSC_ScheduledTask/README.md
+++ b/source/DSCResources/DSC_ScheduledTask/README.md
@@ -6,6 +6,16 @@ scheduled tasks.
 
 ## Known Issues
 
+One of the values needed for the `MultipleInstances` parameter is missing from the
+`Microsoft.PowerShell.Cmdletization.GeneratedTypes.ScheduledTask.MultipleInstancesEnum`
+enumerator. There are four valid values defined for the `MultipleInstances` property of the
+Task Settings ([TaskSettings.MultipleInstances Property](https://docs.microsoft.com/en-us/windows/win32/taskschd/tasksettings-multipleinstances "TaskSettings.MultipleInstances Property")).
+The `MultipleInstancesEnum` enumerator has three values, which can be mapped to three
+of the four valid values, but there is no value corresponding to `TASK_INSTANCES_STOP_EXISTING`.
+The result of this omission is that a workaround is required to
+accommodate the `StopExisting` value for the `MultipleInstances` parameter,
+which would not be necessary if the enumerator had all four valid values.
+
 ### ExecuteAsCredential
 
 #### When Using a BUILTIN Group
diff --git a/tests/Unit/DSC_ScheduledTask.Tests.ps1 b/tests/Unit/DSC_ScheduledTask.Tests.ps1
index a15d4901..a1247c30 100644
--- a/tests/Unit/DSC_ScheduledTask.Tests.ps1
+++ b/tests/Unit/DSC_ScheduledTask.Tests.ps1
@@ -112,7 +112,9 @@ try
                     Verbose            = $true
                 }
 
-                Mock -CommandName Get-ScheduledTask -MockWith { return $null }
+                $scheduledTask = $null
+                Mock -CommandName Get-ScheduledTask -MockWith { return $scheduledTask }
+                Mock -CommandName Register-ScheduledTask
 
                 It 'Should return the correct values from Get-TargetResource' {
                     $result = Get-TargetResource @getTargetResourceParameters
@@ -125,7 +127,9 @@ try
 
                 It 'Should create the scheduled task in the set method' {
                     Set-TargetResource @testParameters
+                    Assert-MockCalled Register-ScheduledTask -Exactly -Times 1
                 }
+
             }
 
             Context 'A scheduled task exists, but it should not' {
@@ -154,6 +158,10 @@ try
                                     CimClassName = 'MSFT_TaskTimeTrigger'
                                 }
                             })
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                         Principal = @{
                             UserId = 'SYSTEM'
                         }
@@ -198,6 +206,7 @@ try
                         }
                         Settings = [pscustomobject] @{
                             Enabled = $true
+                            MultipleInstances = 'StopExisting'
                         }
                     } }
 
@@ -245,6 +254,7 @@ try
                         )
                         Settings = [pscustomobject] @{
                             Enabled = $true
+                            MultipleInstances = 'StopExisting'
                         }
                     }
                 }
@@ -314,6 +324,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                         Principal = [pscustomobject] @{
                             UserId = 'SYSTEM'
                         }
@@ -364,6 +378,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                         Principal = [pscustomobject] @{
                             UserId = 'SYSTEM'
                         }
@@ -409,6 +427,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                         Principal = [pscustomobject] @{
                             UserId = 'SYSTEM'
                         }
@@ -459,6 +481,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                         Principal = [pscustomobject] @{
                             UserId = 'SYSTEM'
                         }
@@ -503,6 +529,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                         Principal = [pscustomobject] @{
                             UserId = 'SYSTEM'
                         }
@@ -549,6 +579,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                         Principal = [pscustomobject] @{
                             UserId = 'SYSTEM'
                         }
@@ -595,6 +629,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                         Principal = [pscustomobject] @{
                             UserId = 'WrongUser'
                         }
@@ -647,6 +685,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                         Principal = [pscustomobject] @{
                             UserId    = 'DEMO\RightUser'
                             LogonType = 'Password'
@@ -701,6 +743,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                         Principal = [pscustomobject] @{
                             UserId   = 'DEMO\RightUser'
                             RunLevel = 'Limited'
@@ -755,6 +801,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                         Principal = [pscustomobject] @{
                             UserId = 'SYSTEM'
                         }
@@ -807,6 +857,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                         Principal = [pscustomobject] @{
                             UserId = 'SYSTEM'
                         }
@@ -859,8 +913,9 @@ try
                                 }
                             }
                         )
-                        Settings  = [pscustomobject] @{
+                        Settings = [pscustomobject] @{
                             Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
                         }
                         Principal = [pscustomobject] @{
                             UserId = 'SYSTEM'
@@ -919,6 +974,7 @@ try
                         Settings  = [pscustomobject] @{
                             Enabled            = $true
                             ExecutionTimeLimit = "PT$([System.TimeSpan]::Parse($testParameters.RepeatInterval).TotalSeconds + 60)S"
+                            MultipleInstances = 'IgnoreNew'
                         }
                         Principal = [pscustomobject] @{
                             UserId = 'SYSTEM'
@@ -986,6 +1042,7 @@ try
                             }
                             ExecutionTimeLimit = "PT$([System.TimeSpan]::Parse($testParameters.ExecutionTimeLimit).TotalMinutes)M"
                             RestartInterval    = "PT$([System.TimeSpan]::Parse($testParameters.RestartInterval).TotalMinutes)M"
+                            MultipleInstances = 'IgnoreNew'
                         }
                         Principal = [pscustomobject] @{
                             UserId = 'SYSTEM'
@@ -1036,6 +1093,7 @@ try
                         )
                         Settings  = [pscustomobject] @{
                             Enabled = $false
+                            MultipleInstances = 'IgnoreNew'
                         }
                         Principal = [pscustomobject] @{
                             UserId = 'SYSTEM'
@@ -1086,6 +1144,7 @@ try
                         )
                         Settings  = [pscustomobject] @{
                             Enabled = $false
+                            MultipleInstances = 'IgnoreNew'
                         }
                         Principal = [pscustomobject] @{
                             UserId = 'SYSTEM'
@@ -1140,6 +1199,7 @@ try
                         )
                         Settings  = [pscustomobject] @{
                             Enabled = $false
+                            MultipleInstances = 'IgnoreNew'
                         }
                         Principal = [pscustomobject] @{
                             UserId = 'SYSTEM'
@@ -1222,6 +1282,7 @@ try
                             }
                             ExecutionTimeLimit = "PT$([System.TimeSpan]::Parse($testParameters.ExecutionTimeLimit).TotalMinutes)M"
                             RestartInterval    = "PT$([System.TimeSpan]::Parse($testParameters.RestartInterval).TotalMinutes)M"
+                            MultipleInstances = 'IgnoreNew'
                         }
                         Principal = [pscustomobject] @{
                             UserId = 'SYSTEM'
@@ -1287,6 +1348,7 @@ try
                             }
                             ExecutionTimeLimit = "PT$([System.TimeSpan]::Parse($testParameters.ExecutionTimeLimit).TotalMinutes)M"
                             RestartInterval    = "PT$([System.TimeSpan]::Parse($testParameters.RestartInterval).TotalMinutes)M"
+                            MultipleInstances = 'IgnoreNew'
                         }
                         Principal = [pscustomobject] @{
                             UserId = 'SYSTEM'
@@ -1339,6 +1401,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                         Principal = [pscustomobject] @{
                             UserId = 'SYSTEM'
                         }
@@ -1390,6 +1456,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                         Principal = [pscustomobject] @{
                             UserId = 'SYSTEM'
                         }
@@ -1441,6 +1511,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                         Principal = [pscustomobject] @{
                             UserId = 'SYSTEM'
                         }
@@ -1481,6 +1555,7 @@ try
                         }
                         Settings = [pscustomobject] @{
                             Enabled = $true
+                            MultipleInstances = 'StopExisting'
                         }
                     }
                 }
@@ -1528,6 +1603,7 @@ try
                         }
                         Settings = [pscustomobject] @{
                             Enabled = $true
+                            MultipleInstances = 'StopExisting'
                         }
                     }
                 }
@@ -1599,6 +1675,7 @@ try
                         }
                         Settings = [pscustomobject] @{
                             Enabled = $true
+                            MultipleInstances = 'StopExisting'
                         }
                     }
                 }
@@ -1652,6 +1729,7 @@ try
                         }
                         Settings = [pscustomobject] @{
                             Enabled = $true
+                            MultipleInstances = 'StopExisting'
                         }
                     }
                 }
@@ -1722,6 +1800,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                         Principal = [pscustomobject] @{
                             UserId    = 'NT AUTHORITY\' + $testParameters.BuiltInAccount
                             LogonType = 'ServiceAccount'
@@ -1792,6 +1874,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                         Principal = [pscustomobject] @{
                             UserId = 'gMSA$'
                         }
@@ -1839,6 +1925,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                         Principal = [pscustomobject] @{
                             UserId = 'update_gMSA$'
                         }
@@ -1892,6 +1982,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                     }
                 }
 
@@ -1922,6 +2016,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                     }
                 }
 
@@ -1966,6 +2064,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                     }
                 }
 
@@ -1996,6 +2098,10 @@ try
                                 }
                             }
                         )
+                        Settings = [pscustomobject] @{
+                            Enabled = $true
+                            MultipleInstances = 'IgnoreNew'
+                        }
                     }
                 }
 
@@ -2030,12 +2136,13 @@ try
             Context 'When a scheduled task is configured with the ScheduleType AtLogon and is in desired state' {
                 $startTimeString = '2018-10-01T01:00:00'
                 $testParameters = $getTargetResourceParameters + @{
-                    ActionExecutable = 'C:\windows\system32\WindowsPowerShell\v1.0\powershell.exe'
-                    StartTime        = Get-Date -Date $startTimeString
-                    ScheduleType     = 'AtLogon'
-                    Delay            = '00:01:00'
-                    Enable           = $true
-                    Verbose          = $true
+                    ActionExecutable  = 'C:\windows\system32\WindowsPowerShell\v1.0\powershell.exe'
+                    StartTime         = Get-Date -Date $startTimeString
+                    ScheduleType      = 'AtLogon'
+                    Delay             = '00:01:00'
+                    Enable            = $true
+                    Verbose           = $true
+                    MultipleInstances = 'StopExisting'
                 }
 
                 Mock -CommandName Get-ScheduledTask -MockWith {
@@ -2058,6 +2165,7 @@ try
                         )
                         Settings = [pscustomobject] @{
                             Enabled = $testParameters.Enable
+                            MultipleInstances = $testParameters.MultipleInstances
                         }
                     }
                 }
@@ -2105,6 +2213,7 @@ try
                         )
                         Settings = [pscustomobject] @{
                             Enabled = $testParameters.Enable
+                            MultipleInstances = 'StopExisting'
                         }
                     }
                 }
@@ -2157,6 +2266,7 @@ try
                         )
                         Settings    = [pscustomobject] @{
                             Enabled = $testParameters.Enable
+                            MultipleInstances = 'IgnoreNew'
                         }
                     }
                 }