diff --git a/stdlib/@tests/test_cases/sqlite3/check_aggregations.py b/stdlib/@tests/test_cases/sqlite3/check_aggregations.py
new file mode 100644
index 000000000000..8eebe71a39e0
--- /dev/null
+++ b/stdlib/@tests/test_cases/sqlite3/check_aggregations.py
@@ -0,0 +1,115 @@
+import sqlite3
+import sys
+
+
+class WindowSumInt:
+    def __init__(self) -> None:
+        self.count = 0
+
+    def step(self, param: int) -> None:
+        self.count += param
+
+    def value(self) -> int:
+        return self.count
+
+    def inverse(self, param: int) -> None:
+        self.count -= param
+
+    def finalize(self) -> int:
+        return self.count
+
+
+con = sqlite3.connect(":memory:")
+cur = con.execute("CREATE TABLE test(x, y)")
+values = [("a", 4), ("b", 5), ("c", 3), ("d", 8), ("e", 1)]
+cur.executemany("INSERT INTO test VALUES(?, ?)", values)
+
+if sys.version_info >= (3, 11):
+    con.create_window_function("sumint", 1, WindowSumInt)
+
+con.create_aggregate("sumint", 1, WindowSumInt)
+cur.execute(
+    """
+    SELECT x, sumint(y) OVER (
+        ORDER BY x ROWS BETWEEN 1 PRECEDING AND 1 FOLLOWING
+    ) AS sum_y
+    FROM test ORDER BY x
+"""
+)
+con.close()
+
+
+def _create_window_function() -> WindowSumInt:
+    return WindowSumInt()
+
+
+# A callable should work as well.
+if sys.version_info >= (3, 11):
+    con.create_window_function("sumint", 1, _create_window_function)
+    con.create_aggregate("sumint", 1, _create_window_function)
+
+# With num_args set to 1, the callable should not be called with more than one.
+
+
+class WindowSumIntMultiArgs:
+    def __init__(self) -> None:
+        self.count = 0
+
+    def step(self, *args: int) -> None:
+        self.count += sum(args)
+
+    def value(self) -> int:
+        return self.count
+
+    def inverse(self, *args: int) -> None:
+        self.count -= sum(args)
+
+    def finalize(self) -> int:
+        return self.count
+
+
+if sys.version_info >= (3, 11):
+    con.create_window_function("sumint", 1, WindowSumIntMultiArgs)
+    con.create_window_function("sumint", 2, WindowSumIntMultiArgs)
+
+con.create_aggregate("sumint", 1, WindowSumIntMultiArgs)
+con.create_aggregate("sumint", 2, WindowSumIntMultiArgs)
+
+
+class WindowSumIntMismatchedArgs:
+    def __init__(self) -> None:
+        self.count = 0
+
+    def step(self, *args: str) -> None:
+        self.count += 34
+
+    def value(self) -> int:
+        return self.count
+
+    def inverse(self, *args: int) -> None:
+        self.count -= 34
+
+    def finalize(self) -> str:
+        return str(self.count)
+
+
+# Since the types for `inverse`, `step`, `finalize`, and `value` are not compatible, the following should fail.
+if sys.version_info >= (3, 11):
+    con.create_window_function("sumint", 1, WindowSumIntMismatchedArgs)  # type: ignore
+    con.create_window_function("sumint", 2, WindowSumIntMismatchedArgs)  # type: ignore
+
+
+class AggMismatchedArgs:
+    def __init__(self) -> None:
+        self.count = 0
+
+    def step(self, *args: str) -> None:
+        self.count += 34
+
+    def finalize(self) -> int:
+        return self.count
+
+
+# Since the types for `step` and `finalize` are not compatible, the following should fail.
+con.create_aggregate("sumint", 1, AggMismatchedArgs)  # type: ignore
+con.create_aggregate("sumint", 2, AggMismatchedArgs)  # type: ignore
diff --git a/stdlib/@tests/test_cases/check_sqlite3.py b/stdlib/@tests/test_cases/sqlite3/check_connection.py
similarity index 100%
rename from stdlib/@tests/test_cases/check_sqlite3.py
rename to stdlib/@tests/test_cases/sqlite3/check_connection.py
diff --git a/stdlib/sqlite3/dbapi2.pyi b/stdlib/sqlite3/dbapi2.pyi
index 3cb4b93e88fe..0fd7740804dd 100644
--- a/stdlib/sqlite3/dbapi2.pyi
+++ b/stdlib/sqlite3/dbapi2.pyi
@@ -11,6 +11,7 @@ _T = TypeVar("_T")
 _ConnectionT = TypeVar("_ConnectionT", bound=Connection)
 _CursorT = TypeVar("_CursorT", bound=Cursor)
 _SqliteData: TypeAlias = str | ReadableBuffer | int | float | None
+_SQLType = TypeVar("_SQLType", bound=_SqliteData)
 # Data that is passed through adapters can be of any type accepted by an adapter.
 _AdaptedInputData: TypeAlias = _SqliteData | Any
 # The Mapping must really be a dict, but making it invariant is too annoying.
@@ -312,27 +313,25 @@ else:
     def register_adapter(type: type[_T], caster: _Adapter[_T], /) -> None: ...
     def register_converter(name: str, converter: _Converter, /) -> None: ...
 
-class _AggregateProtocol(Protocol):
-    def step(self, value: int, /) -> object: ...
-    def finalize(self) -> int: ...
+class _SingleParamAggregateProtocol(Protocol[_SQLType]):
+    def step(self, param: _SQLType, /) -> object: ...
+    def finalize(self) -> _SQLType: ...
 
-class _SingleParamWindowAggregateClass(Protocol):
-    def step(self, param: Any, /) -> object: ...
-    def inverse(self, param: Any, /) -> object: ...
-    def value(self) -> _SqliteData: ...
-    def finalize(self) -> _SqliteData: ...
+class _AnyParamAggregateProtocol(Protocol[_SQLType]):
+    def step(self, *args: _SQLType) -> object: ...
+    def finalize(self) -> _SQLType: ...
 
-class _AnyParamWindowAggregateClass(Protocol):
-    def step(self, *args: Any) -> object: ...
-    def inverse(self, *args: Any) -> object: ...
-    def value(self) -> _SqliteData: ...
-    def finalize(self) -> _SqliteData: ...
+class _SingleParamWindowAggregateClass(Protocol[_SQLType]):
+    def step(self, param: _SQLType, /) -> object: ...
+    def inverse(self, param: _SQLType, /) -> object: ...
+    def value(self) -> _SQLType: ...
+    def finalize(self) -> _SQLType: ...
 
-class _WindowAggregateClass(Protocol):
-    step: Callable[..., object]
-    inverse: Callable[..., object]
-    def value(self) -> _SqliteData: ...
-    def finalize(self) -> _SqliteData: ...
+class _AnyParamWindowAggregateClass(Protocol[_SQLType]):
+    def step(self, *args: _SQLType) -> object: ...
+    def inverse(self, *args: _SQLType) -> object: ...
+    def value(self) -> _SQLType: ...
+    def finalize(self) -> _SQLType: ...
 
 class Connection:
     @property
@@ -398,22 +397,30 @@ class Connection:
         def blobopen(self, table: str, column: str, row: int, /, *, readonly: bool = False, name: str = "main") -> Blob: ...
 
     def commit(self) -> None: ...
-    def create_aggregate(self, name: str, n_arg: int, aggregate_class: Callable[[], _AggregateProtocol]) -> None: ...
+    @overload
+    def create_aggregate(
+        self, name: str, n_arg: Literal[1], aggregate_class: Callable[[], _SingleParamAggregateProtocol[_SQLType]]
+    ) -> None: ...
+    @overload
+    def create_aggregate(
+        self, name: str, n_arg: int, aggregate_class: Callable[[], _AnyParamAggregateProtocol[_SQLType]]
+    ) -> None: ...
+
     if sys.version_info >= (3, 11):
         # num_params determines how many params will be passed to the aggregate class. We provide an overload
         # for the case where num_params = 1, which is expected to be the common case.
         @overload
         def create_window_function(
-            self, name: str, num_params: Literal[1], aggregate_class: Callable[[], _SingleParamWindowAggregateClass] | None, /
+            self,
+            name: str,
+            num_params: Literal[1],
+            aggregate_class: Callable[[], _SingleParamWindowAggregateClass[_SQLType]] | None,
+            /,
         ) -> None: ...
         # And for num_params = -1, which means the aggregate must accept any number of parameters.
         @overload
         def create_window_function(
-            self, name: str, num_params: Literal[-1], aggregate_class: Callable[[], _AnyParamWindowAggregateClass] | None, /
-        ) -> None: ...
-        @overload
-        def create_window_function(
-            self, name: str, num_params: int, aggregate_class: Callable[[], _WindowAggregateClass] | None, /
+            self, name: str, num_params: int, aggregate_class: Callable[[], _AnyParamWindowAggregateClass[_SQLType]] | None, /
         ) -> None: ...
 
     def create_collation(self, name: str, callback: Callable[[str, str], int | SupportsIndex] | None, /) -> None: ...