diff --git a/xarray/tests/test_distributed.py b/xarray/tests/test_distributed.py
index fb917dfb254..6a8cd9c457b 100644
--- a/xarray/tests/test_distributed.py
+++ b/xarray/tests/test_distributed.py
@@ -126,7 +126,8 @@ def test_dask_distributed_write_netcdf_with_dimensionless_variables(
 
 @requires_cftime
 @requires_netCDF4
-def test_open_mfdataset_can_open_files_with_cftime_index(tmp_path):
+@pytest.mark.parametrize("parallel", (True, False))
+def test_open_mfdataset_can_open_files_with_cftime_index(parallel, tmp_path):
     T = xr.cftime_range("20010101", "20010501", calendar="360_day")
     Lon = np.arange(100)
     data = np.random.random((T.size, Lon.size))
@@ -135,9 +136,55 @@ def test_open_mfdataset_can_open_files_with_cftime_index(tmp_path):
     da.to_netcdf(file_path)
     with cluster() as (s, [a, b]):
         with Client(s["address"]):
-            for parallel in (False, True):
-                with xr.open_mfdataset(file_path, parallel=parallel) as tf:
-                    assert_identical(tf["test"], da)
+            with xr.open_mfdataset(file_path, parallel=parallel) as tf:
+                assert_identical(tf["test"], da)
+
+
+@requires_cftime
+@requires_netCDF4
+@pytest.mark.parametrize("parallel", (True, False))
+def test_open_mfdataset_multiple_files_parallel_distributed(parallel, tmp_path):
+    lon = np.arange(100)
+    time = xr.cftime_range("20010101", periods=100, calendar="360_day")
+    data = np.random.random((time.size, lon.size))
+    da = xr.DataArray(data, coords={"time": time, "lon": lon}, name="test")
+
+    fnames = []
+    for i in range(0, 100, 10):
+        fname = tmp_path / f"test_{i}.nc"
+        da.isel(time=slice(i, i + 10)).to_netcdf(fname)
+        fnames.append(fname)
+
+    with cluster() as (s, [a, b]):
+        with Client(s["address"]):
+            with xr.open_mfdataset(
+                fnames, parallel=parallel, concat_dim="time", combine="nested"
+            ) as tf:
+                assert_identical(tf["test"], da)
+
+
+# TODO: move this to test_backends.py
+@requires_cftime
+@requires_netCDF4
+@pytest.mark.parametrize("parallel", (True, False))
+def test_open_mfdataset_multiple_files_parallel(parallel, tmp_path):
+    lon = np.arange(100)
+    time = xr.cftime_range("20010101", periods=100, calendar="360_day")
+    data = np.random.random((time.size, lon.size))
+    da = xr.DataArray(data, coords={"time": time, "lon": lon}, name="test")
+
+    fnames = []
+    for i in range(0, 100, 10):
+        fname = tmp_path / f"test_{i}.nc"
+        da.isel(time=slice(i, i + 10)).to_netcdf(fname)
+        fnames.append(fname)
+
+    for get in [dask.threaded.get, dask.multiprocessing.get, dask.local.get_sync, None]:
+        with dask.config.set(scheduler=get):
+            with xr.open_mfdataset(
+                fnames, parallel=parallel, concat_dim="time", combine="nested"
+            ) as tf:
+                assert_identical(tf["test"], da)
 
 
 @pytest.mark.parametrize("engine,nc_format", ENGINES_AND_FORMATS)