diff --git a/mypy/checkexpr.py b/mypy/checkexpr.py
index 286ef0dab6ae..2f872212640a 100644
--- a/mypy/checkexpr.py
+++ b/mypy/checkexpr.py
@@ -2278,6 +2278,22 @@ def get_arg_infer_passes(
                     #   run(test, 1, 2)
                     # we will use `test` for inference, since it will allow to infer also
                     # argument *names* for P <: [x: int, y: int].
+                    if isinstance(p_actual, UnionType):
+                        new_items = []
+                        for item in p_actual.items:
+                            # narrow the union based on some approximations
+                            p_item = get_proper_type(item)
+                            if isinstance(p_item, CallableType) or (
+                                isinstance(p_item, Instance)
+                                and find_member("__call__", p_item, p_item, is_operator=True)
+                                is not None
+                            ):
+                                new_items.append(p_item)
+                                if len(new_items) == 2:
+                                    break
+
+                        if len(new_items) == 1:
+                            p_actual = new_items[0]
                     if isinstance(p_actual, Instance):
                         call_method = find_member("__call__", p_actual, p_actual, is_operator=True)
                         if call_method is not None:
diff --git a/mypy/typeops.py b/mypy/typeops.py
index 1667e8431a17..0afaaa9a7a3c 100644
--- a/mypy/typeops.py
+++ b/mypy/typeops.py
@@ -458,21 +458,20 @@ def callable_corresponding_argument(
     if by_name is not None and by_pos is not None:
         if by_name == by_pos:
             return by_name
-        # If we're dealing with an optional pos-only and an optional
-        # name-only arg, merge them.  This is the case for all functions
-        # taking both *args and **args, or a pair of functions like so:
+        # If we're dealing with an optional pos and an optional
+        # name arg, merge them.  This is the case for all functions
+        # taking both *args and **args, or a functions like so:
 
         # def right(a: int = ...) -> None: ...
-        # def left(__a: int = ..., *, a: int = ...) -> None: ...
-        from mypy.subtypes import is_equivalent
+        # def left1(__a: int = ..., *, a: int = ...) -> None: ...
+        # def left2(x: int = ..., a: int = ...) -> None: ...
 
-        if (
-            not (by_name.required or by_pos.required)
-            and by_pos.name is None
-            and by_name.pos is None
-            and is_equivalent(by_name.typ, by_pos.typ)
-        ):
-            return FormalArgument(by_name.name, by_pos.pos, by_name.typ, False)
+        from mypy.meet import meet_types
+
+        if not (by_name.required or by_pos.required):
+            return FormalArgument(
+                by_name.name, by_pos.pos, meet_types(by_pos.typ, by_name.typ), False
+            )
     return by_name if by_name is not None else by_pos
 
 
diff --git a/test-data/unit/check-overloading.test b/test-data/unit/check-overloading.test
index 2092f99487b0..949f6d3053f8 100644
--- a/test-data/unit/check-overloading.test
+++ b/test-data/unit/check-overloading.test
@@ -6768,3 +6768,34 @@ class D(Generic[T]):
 a: D[str]  # E: Type argument "str" of "D" must be a subtype of "C"
 reveal_type(a.f(1))  # N: Revealed type is "builtins.int"
 reveal_type(a.f("x"))  # N: Revealed type is "builtins.str"
+
+[case testOverloadWithTwoRelevantArgsWithDifferentType]
+from typing import overload, Union
+
+@overload
+def set(year: int) -> None:
+    ...
+
+@overload
+def set() -> None:
+    ...
+
+# no error here:
+def set(*args: object, **kw: int) -> None:
+    pass
+[builtins fixtures/tuple.pyi]
+
+[case testOverloadWithTwoRelevantOptionalArgs]
+from typing import overload
+
+@overload
+def set(year: int) -> None:
+    ...
+
+@overload
+def set() -> None:
+    ...
+
+# no error:
+def set(x: int = 42, year: int = 42) -> None:
+    pass
diff --git a/test-data/unit/check-parameter-specification.test b/test-data/unit/check-parameter-specification.test
index 5530bc0ecbf9..d61f3f9b4536 100644
--- a/test-data/unit/check-parameter-specification.test
+++ b/test-data/unit/check-parameter-specification.test
@@ -2560,3 +2560,21 @@ def fn(f: MiddlewareFactory[P]) -> Capture[P]: ...
 
 reveal_type(fn(ServerErrorMiddleware))  # N: Revealed type is "__main__.Capture[[handler: Union[builtins.str, None] =, debug: builtins.bool =]]"
 [builtins fixtures/paramspec.pyi]
+
+[case testParamSpecInferenceWithAny]
+from typing_extensions import ParamSpec
+from typing import Any, Callable, Union
+
+P = ParamSpec("P")
+
+def into(f: Callable[P, None], *args: P.args, **kwargs: P.kwargs) -> None:
+    return None
+
+class C:
+    def f(self, y: bool = False, *, x: int = 42) -> None:
+        return None
+
+ex: Union[C, Any] = C()
+
+into(ex.f, x=-1)
+[builtins fixtures/paramspec.pyi]