diff --git a/stdlib/@tests/test_cases/check_functools.py b/stdlib/@tests/test_cases/check_functools.py
index a25c0111adf9..5ce2bfad9599 100644
--- a/stdlib/@tests/test_cases/check_functools.py
+++ b/stdlib/@tests/test_cases/check_functools.py
@@ -1,6 +1,6 @@
 from __future__ import annotations
 
-from functools import cache, cached_property, wraps
+from functools import cache, cached_property, singledispatch, wraps
 from typing import Callable, TypeVar
 from typing_extensions import ParamSpec, assert_type
 
@@ -108,3 +108,31 @@ class CachedChild(CachedParent):
     @cache
     def method(self) -> Child:
         return Child()
+
+
+def check_singledispatch_simple() -> None:
+    @singledispatch
+    def sd_fun(arg: object) -> str:
+        return ""
+
+    @sd_fun.register
+    def _(int_arg: int) -> str:
+        return ""
+
+    sd_fun.dispatch(42)
+    sd_fun.dispatch("")
+    sd_fun.dispatch(1, 2)  # type: ignore
+
+
+def check_singledispatch_additional_args() -> None:
+    @singledispatch
+    def sd_fun(arg: object, posonly: str, /, verbose: bool = False) -> str:
+        return ""
+
+    @sd_fun.register
+    def _(int_arg: int, posonly: str, /, verbose: bool = False) -> str:
+        return ""
+
+    sd_fun.dispatch(5.4, "")
+    sd_fun.dispatch(5.4, "", verbose=True)
+    sd_fun.dispatch(1, 2)  # type: ignore
diff --git a/stdlib/functools.pyi b/stdlib/functools.pyi
index 57bc3f179f7a..adbdd7d83cec 100644
--- a/stdlib/functools.pyi
+++ b/stdlib/functools.pyi
@@ -4,7 +4,7 @@ from _typeshed import SupportsAllComparisons, SupportsItems
 from collections.abc import Callable, Hashable, Iterable, Sized
 from types import GenericAlias
 from typing import Any, Final, Generic, Literal, NamedTuple, TypedDict, TypeVar, final, overload, type_check_only
-from typing_extensions import ParamSpec, Self, TypeAlias, disjoint_base
+from typing_extensions import Concatenate, ParamSpec, Self, TypeAlias, disjoint_base
 
 __all__ = [
     "update_wrapper",
@@ -26,6 +26,8 @@ __all__ = [
 _T = TypeVar("_T")
 _T_co = TypeVar("_T_co", covariant=True)
 _S = TypeVar("_S")
+_P = ParamSpec("_P", default=...)
+_R = TypeVar("_R", default=Any)
 _PWrapped = ParamSpec("_PWrapped")
 _RWrapped = TypeVar("_RWrapped")
 _PWrapper = ParamSpec("_PWrapper")
@@ -189,44 +191,69 @@ class partialmethod(Generic[_T]):
     def __isabstractmethod__(self) -> bool: ...
     def __class_getitem__(cls, item: Any, /) -> GenericAlias: ...
 
-if sys.version_info >= (3, 11):
-    _RegType: TypeAlias = type[Any] | types.UnionType
-else:
-    _RegType: TypeAlias = type[Any]
-
 @type_check_only
-class _SingleDispatchCallable(Generic[_T]):
-    registry: types.MappingProxyType[Any, Callable[..., _T]]
-    def dispatch(self, cls: Any) -> Callable[..., _T]: ...
+class _SingleDispatchCallable(Generic[_P, _R]):
+    # First argument pf the callables in the registry is the type to dispatch on.
+    registry: types.MappingProxyType[Any, Callable[Concatenate[Any, _P], _R]]
+    def dispatch(self, cls: type[_S]) -> Callable[Concatenate[_S, _P], _R]: ...
+    if sys.version_info >= (3, 11):
+        # @fun.register(complex | str)
+        # def _(arg, verbose=False): ...
+        @overload
+        def register(
+            self, cls: types.UnionType, func: None = None
+        ) -> Callable[[Callable[Concatenate[_S, _P], _R]], Callable[Concatenate[_S, _P], _R]]: ...
     # @fun.register(complex)
     # def _(arg, verbose=False): ...
     @overload
-    def register(self, cls: _RegType, func: None = None) -> Callable[[Callable[..., _T]], Callable[..., _T]]: ...
+    def register(  # type: ignore[overload-overlap]
+        self, cls: type[_S], func: None = None
+    ) -> Callable[[Callable[Concatenate[_S, _P], _R]], Callable[Concatenate[_S, _P], _R]]: ...
     # @fun.register
     # def _(arg: int, verbose=False):
     @overload
-    def register(self, cls: Callable[..., _T], func: None = None) -> Callable[..., _T]: ...
+    def register(self, cls: Callable[Concatenate[_S, _P], _R], func: None = None) -> Callable[Concatenate[_S, _P], _R]: ...
+    if sys.version_info >= (3, 11):
+        # fun.register(int, lambda x: x)
+        @overload
+        def register(
+            self, cls: types.UnionType, func: Callable[Concatenate[_S, _P], _R]
+        ) -> Callable[Concatenate[_S, _P], _R]: ...
     # fun.register(int, lambda x: x)
     @overload
-    def register(self, cls: _RegType, func: Callable[..., _T]) -> Callable[..., _T]: ...
+    def register(self, cls: type[_S], func: Callable[Concatenate[_S, _P], _R]) -> Callable[Concatenate[_S, _P], _R]: ...
     def _clear_cache(self) -> None: ...
-    def __call__(self, /, *args: Any, **kwargs: Any) -> _T: ...
+    def __call__(self, arg: object, /, *args: _P.args, **kwargs: _P.kwargs) -> _R: ...
 
-def singledispatch(func: Callable[..., _T]) -> _SingleDispatchCallable[_T]: ...
+def singledispatch(func: Callable[Concatenate[object, _P], _R]) -> _SingleDispatchCallable[_P, _R]: ...
 
-class singledispatchmethod(Generic[_T]):
-    dispatcher: _SingleDispatchCallable[_T]
-    func: Callable[..., _T]
-    def __init__(self, func: Callable[..., _T]) -> None: ...
+class singledispatchmethod(Generic[_P, _R]):
+    dispatcher: _SingleDispatchCallable[_P, _R]
+    func: Callable[_P, _R]
+    def __init__(self, func: Callable[Concatenate[object, _P], _R]) -> None: ...
     @property
     def __isabstractmethod__(self) -> bool: ...
+    if sys.version_info >= (3, 11):
+        @overload
+        def register(
+            self, cls: types.UnionType, method: None = None
+        ) -> Callable[[Callable[Concatenate[_S, _P], _R]], Callable[Concatenate[_S, _P], _R]]: ...
+
     @overload
-    def register(self, cls: _RegType, method: None = None) -> Callable[[Callable[..., _T]], Callable[..., _T]]: ...
+    def register(  # type: ignore[overload-overlap]
+        self, cls: type[_S], method: None = None
+    ) -> Callable[[Callable[Concatenate[_S, _P], _R]], Callable[Concatenate[_S, _P], _R]]: ...
     @overload
-    def register(self, cls: Callable[..., _T], method: None = None) -> Callable[..., _T]: ...
+    def register(self, cls: Callable[Concatenate[_S, _P], _R], method: None = None) -> Callable[Concatenate[_S, _P], _R]: ...
+    if sys.version_info >= (3, 11):
+        @overload
+        def register(
+            self, cls: types.UnionType, method: Callable[Concatenate[_S, _P], _R]
+        ) -> Callable[Concatenate[_S, _P], _R]: ...
+
     @overload
-    def register(self, cls: _RegType, method: Callable[..., _T]) -> Callable[..., _T]: ...
-    def __get__(self, obj: _S, cls: type[_S] | None = None) -> Callable[..., _T]: ...
+    def register(self, cls: type[_S], method: Callable[Concatenate[_S, _P], _R]) -> Callable[Concatenate[_S, _P], _R]: ...
+    def __get__(self, obj: _S, cls: type[_S] | None = None) -> Callable[Concatenate[_S, _P], _R]: ...
 
 class cached_property(Generic[_T_co]):
     func: Callable[[Any], _T_co]
diff --git a/stubs/aiofiles/aiofiles/threadpool/__init__.pyi b/stubs/aiofiles/aiofiles/threadpool/__init__.pyi
index 51cb1d2fd8bd..554cd6ea1109 100644
--- a/stubs/aiofiles/aiofiles/threadpool/__init__.pyi
+++ b/stubs/aiofiles/aiofiles/threadpool/__init__.pyi
@@ -99,7 +99,7 @@ def open(
     executor: Executor | None = None,
 ) -> AiofilesContextManager[_UnknownAsyncBinaryIO]: ...
 
-wrap: _SingleDispatchCallable[Any]
+wrap: _SingleDispatchCallable[Any, Any]
 
 stdin: AsyncTextIndirectIOWrapper
 stdout: AsyncTextIndirectIOWrapper