diff --git a/mypy/checker.py b/mypy/checker.py
index 5a74f019dcf4..95a65b0a8cd1 100644
--- a/mypy/checker.py
+++ b/mypy/checker.py
@@ -1208,7 +1208,9 @@ def check_func_def(
                     ):
                         if defn.is_class or defn.name == "__new__":
                             ref_type = mypy.types.TypeType.make_normalized(ref_type)
-                        erased = get_proper_type(erase_to_bound(arg_type))
+                        # This level of erasure matches the one in checkmember.check_self_arg(),
+                        # better keep these two checks consistent.
+                        erased = get_proper_type(erase_typevars(erase_to_bound(arg_type)))
                         if not is_subtype(ref_type, erased, ignore_type_params=True):
                             if (
                                 isinstance(erased, Instance)
diff --git a/mypy/checkmember.py b/mypy/checkmember.py
index 60430839ff62..59af0d402e14 100644
--- a/mypy/checkmember.py
+++ b/mypy/checkmember.py
@@ -896,6 +896,8 @@ def f(self: S) -> T: ...
             return functype
         else:
             selfarg = get_proper_type(item.arg_types[0])
+            # This level of erasure matches the one in checker.check_func_def(),
+            # better keep these two checks consistent.
             if subtypes.is_subtype(dispatched_arg_type, erase_typevars(erase_to_bound(selfarg))):
                 new_items.append(item)
             elif isinstance(selfarg, ParamSpecType):
diff --git a/mypy/messages.py b/mypy/messages.py
index b6fdaf06a8e0..8bc190b7d66d 100644
--- a/mypy/messages.py
+++ b/mypy/messages.py
@@ -2132,6 +2132,9 @@ def report_protocol_problems(
             not is_subtype(subtype, erase_type(supertype), options=self.options)
             or not subtype.type.defn.type_vars
             or not supertype.type.defn.type_vars
+            # Always show detailed message for ParamSpec
+            or subtype.type.has_param_spec_type
+            or supertype.type.has_param_spec_type
         ):
             type_name = format_type(subtype, self.options, module_names=True)
             self.note(f"Following member(s) of {type_name} have conflicts:", context, code=code)
diff --git a/mypy/subtypes.py b/mypy/subtypes.py
index fdde1c24670e..e8339a8c4d69 100644
--- a/mypy/subtypes.py
+++ b/mypy/subtypes.py
@@ -1519,6 +1519,18 @@ def are_trivial_parameters(param: Parameters | NormalizedCallableType) -> bool:
     )
 
 
+def is_trivial_suffix(param: Parameters | NormalizedCallableType) -> bool:
+    param_star = param.var_arg()
+    param_star2 = param.kw_arg()
+    return (
+        param.arg_kinds[-2:] == [ARG_STAR, ARG_STAR2]
+        and param_star is not None
+        and isinstance(get_proper_type(param_star.typ), AnyType)
+        and param_star2 is not None
+        and isinstance(get_proper_type(param_star2.typ), AnyType)
+    )
+
+
 def are_parameters_compatible(
     left: Parameters | NormalizedCallableType,
     right: Parameters | NormalizedCallableType,
@@ -1540,6 +1552,7 @@ def are_parameters_compatible(
     # Treat "def _(*a: Any, **kw: Any) -> X" similarly to "Callable[..., X]"
     if are_trivial_parameters(right):
         return True
+    trivial_suffix = is_trivial_suffix(right)
 
     # Match up corresponding arguments and check them for compatibility. In
     # every pair (argL, argR) of corresponding arguments from L and R, argL must
@@ -1570,7 +1583,7 @@ def _incompatible(left_arg: FormalArgument | None, right_arg: FormalArgument | N
         if right_arg is None:
             return False
         if left_arg is None:
-            return not allow_partial_overlap
+            return not allow_partial_overlap and not trivial_suffix
         return not is_compat(right_arg.typ, left_arg.typ)
 
     if _incompatible(left_star, right_star) or _incompatible(left_star2, right_star2):
@@ -1594,7 +1607,7 @@ def _incompatible(left_arg: FormalArgument | None, right_arg: FormalArgument | N
     #           arguments. Get all further positional args of left, and make sure
     #           they're more general than the corresponding member in right.
     # TODO: are we handling UnpackType correctly here?
-    if right_star is not None:
+    if right_star is not None and not trivial_suffix:
         # Synthesize an anonymous formal argument for the right
         right_by_position = right.try_synthesizing_arg_from_vararg(None)
         assert right_by_position is not None
@@ -1621,7 +1634,7 @@ def _incompatible(left_arg: FormalArgument | None, right_arg: FormalArgument | N
     # Phase 1d: Check kw args. Right has an infinite series of optional named
     #           arguments. Get all further named args of left, and make sure
     #           they're more general than the corresponding member in right.
-    if right_star2 is not None:
+    if right_star2 is not None and not trivial_suffix:
         right_names = {name for name in right.arg_names if name is not None}
         left_only_names = set()
         for name, kind in zip(left.arg_names, left.arg_kinds):
diff --git a/mypy/typeops.py b/mypy/typeops.py
index 3f50232f04c1..10efa32c4b91 100644
--- a/mypy/typeops.py
+++ b/mypy/typeops.py
@@ -251,6 +251,10 @@ def supported_self_type(typ: ProperType) -> bool:
     """
     if isinstance(typ, TypeType):
         return supported_self_type(typ.item)
+    if isinstance(typ, CallableType):
+        # Special case: allow class callable instead of Type[...] as cls annotation,
+        # as well as callable self for callback protocols.
+        return True
     return isinstance(typ, TypeVarType) or (
         isinstance(typ, Instance) and typ != fill_typevars(typ.type)
     )
diff --git a/test-data/unit/check-callable.test b/test-data/unit/check-callable.test
index 07c42de74bb3..8a611a689be5 100644
--- a/test-data/unit/check-callable.test
+++ b/test-data/unit/check-callable.test
@@ -598,3 +598,34 @@ a: A
 a()  # E: Missing positional argument "other" in call to "__call__" of "A"
 a(a)
 a(lambda: None)
+
+[case testCallableSubtypingTrivialSuffix]
+from typing import Any, Protocol
+
+class Call(Protocol):
+    def __call__(self, x: int, *args: Any, **kwargs: Any) -> None: ...
+
+def f1() -> None: ...
+a1: Call = f1  # E: Incompatible types in assignment (expression has type "Callable[[], None]", variable has type "Call") \
+               # N: "Call.__call__" has type "Callable[[Arg(int, 'x'), VarArg(Any), KwArg(Any)], None]"
+def f2(x: str) -> None: ...
+a2: Call = f2  # E: Incompatible types in assignment (expression has type "Callable[[str], None]", variable has type "Call") \
+               # N: "Call.__call__" has type "Callable[[Arg(int, 'x'), VarArg(Any), KwArg(Any)], None]"
+def f3(y: int) -> None: ...
+a3: Call = f3  # E: Incompatible types in assignment (expression has type "Callable[[int], None]", variable has type "Call") \
+               # N: "Call.__call__" has type "Callable[[Arg(int, 'x'), VarArg(Any), KwArg(Any)], None]"
+def f4(x: int) -> None: ...
+a4: Call = f4
+
+def f5(x: int, y: int) -> None: ...
+a5: Call = f5
+
+def f6(x: int, y: int = 0) -> None: ...
+a6: Call = f6
+
+def f7(x: int, *, y: int) -> None: ...
+a7: Call = f7
+
+def f8(x: int, *args: int, **kwargs: str) -> None: ...
+a8: Call = f8
+[builtins fixtures/tuple.pyi]
diff --git a/test-data/unit/check-modules.test b/test-data/unit/check-modules.test
index 3da5996ed274..94368f6c1113 100644
--- a/test-data/unit/check-modules.test
+++ b/test-data/unit/check-modules.test
@@ -3193,7 +3193,7 @@ from test1 import aaaa  # E: Module "test1" has no attribute "aaaa"
 import b
 [file a.py]
 class Foo:
-    def frobnicate(self, x, *args, **kwargs): pass
+    def frobnicate(self, x: str, *args, **kwargs): pass
 [file b.py]
 from a import Foo
 class Bar(Foo):
@@ -3201,21 +3201,21 @@ class Bar(Foo):
 [file b.py.2]
 from a import Foo
 class Bar(Foo):
-    def frobnicate(self, *args) -> None: pass
+    def frobnicate(self, *args: int) -> None: pass
 [file b.py.3]
 from a import Foo
 class Bar(Foo):
-    def frobnicate(self, *args) -> None: pass # type: ignore[override] # I know
+    def frobnicate(self, *args: int) -> None: pass # type: ignore[override] # I know
 [builtins fixtures/dict.pyi]
 [out1]
 tmp/b.py:3: error: Signature of "frobnicate" incompatible with supertype "Foo"
 tmp/b.py:3: note:      Superclass:
-tmp/b.py:3: note:          def frobnicate(self, x: Any, *args: Any, **kwargs: Any) -> Any
+tmp/b.py:3: note:          def frobnicate(self, x: str, *args: Any, **kwargs: Any) -> Any
 tmp/b.py:3: note:      Subclass:
 tmp/b.py:3: note:          def frobnicate(self) -> None
 [out2]
 tmp/b.py:3: error: Signature of "frobnicate" incompatible with supertype "Foo"
 tmp/b.py:3: note:      Superclass:
-tmp/b.py:3: note:          def frobnicate(self, x: Any, *args: Any, **kwargs: Any) -> Any
+tmp/b.py:3: note:          def frobnicate(self, x: str, *args: Any, **kwargs: Any) -> Any
 tmp/b.py:3: note:      Subclass:
-tmp/b.py:3: note:          def frobnicate(self, *args: Any) -> None
+tmp/b.py:3: note:          def frobnicate(self, *args: int) -> None
diff --git a/test-data/unit/check-parameter-specification.test b/test-data/unit/check-parameter-specification.test
index d80069644194..da831d29dd43 100644
--- a/test-data/unit/check-parameter-specification.test
+++ b/test-data/unit/check-parameter-specification.test
@@ -1729,7 +1729,12 @@ class A(Protocol[P]):
         ...
 
 def bar(b: A[P]) -> A[Concatenate[int, P]]:
-    return b  # E: Incompatible return value type (got "A[P]", expected "A[[int, **P]]")
+    return b  # E: Incompatible return value type (got "A[P]", expected "A[[int, **P]]") \
+              # N: Following member(s) of "A[P]" have conflicts: \
+              # N:     Expected: \
+              # N:         def foo(self, int, /, *args: P.args, **kwargs: P.kwargs) -> Any \
+              # N:     Got: \
+              # N:         def foo(self, *args: P.args, **kwargs: P.kwargs) -> Any
 [builtins fixtures/paramspec.pyi]
 
 [case testParamSpecPrefixSubtypingValidNonStrict]
@@ -1825,6 +1830,138 @@ c: C[int, [int, str], str]  # E: Nested parameter specifications are not allowed
 reveal_type(c)  # N: Revealed type is "__main__.C[Any]"
 [builtins fixtures/paramspec.pyi]
 
+[case testParamSpecConcatenateSelfType]
+from typing import Callable
+from typing_extensions import ParamSpec, Concatenate
+
+P = ParamSpec("P")
+class A:
+    def __init__(self, a_param_1: str) -> None: ...
+
+    @classmethod
+    def add_params(cls: Callable[P, A]) -> Callable[Concatenate[float, P], A]:
+        def new_constructor(i: float, *args: P.args, **kwargs: P.kwargs) -> A:
+            return cls(*args, **kwargs)
+        return new_constructor
+
+    @classmethod
+    def remove_params(cls: Callable[Concatenate[str, P], A]) -> Callable[P, A]:
+        def new_constructor(*args: P.args, **kwargs: P.kwargs) -> A:
+            return cls("my_special_str", *args, **kwargs)
+        return new_constructor
+
+reveal_type(A.add_params())  # N: Revealed type is "def (builtins.float, a_param_1: builtins.str) -> __main__.A"
+reveal_type(A.remove_params())  # N: Revealed type is "def () -> __main__.A"
+[builtins fixtures/paramspec.pyi]
+
+[case testParamSpecConcatenateCallbackProtocol]
+from typing import Protocol, TypeVar
+from typing_extensions import ParamSpec, Concatenate
+
+P = ParamSpec("P")
+R = TypeVar("R", covariant=True)
+
+class Path: ...
+
+class Function(Protocol[P, R]):
+    def __call__(self, *args: P.args, **kwargs: P.kwargs) -> R: ...
+
+def file_cache(fn: Function[Concatenate[Path, P], R]) -> Function[P, R]:
+    def wrapper(*args: P.args, **kw: P.kwargs) -> R:
+        return fn(Path(), *args, **kw)
+    return wrapper
+
+@file_cache
+def get_thing(path: Path, *, some_arg: int) -> int: ...
+reveal_type(get_thing)  # N: Revealed type is "__main__.Function[[*, some_arg: builtins.int], builtins.int]"
+get_thing(some_arg=1)  # OK
+[builtins fixtures/paramspec.pyi]
+
+[case testParamSpecConcatenateKeywordOnly]
+from typing import Callable, TypeVar
+from typing_extensions import ParamSpec, Concatenate
+
+P = ParamSpec("P")
+R = TypeVar("R")
+
+class Path: ...
+
+def file_cache(fn: Callable[Concatenate[Path, P], R]) -> Callable[P, R]:
+    def wrapper(*args: P.args, **kw: P.kwargs) -> R:
+        return fn(Path(), *args, **kw)
+    return wrapper
+
+@file_cache
+def get_thing(path: Path, *, some_arg: int) -> int: ...
+reveal_type(get_thing)  # N: Revealed type is "def (*, some_arg: builtins.int) -> builtins.int"
+get_thing(some_arg=1)  # OK
+[builtins fixtures/paramspec.pyi]
+
+[case testParamSpecConcatenateCallbackApply]
+from typing import Callable, Protocol
+from typing_extensions import ParamSpec, Concatenate
+
+P = ParamSpec("P")
+
+class FuncType(Protocol[P]):
+    def __call__(self, x: int, s: str, *args: P.args, **kw_args: P.kwargs) -> str: ...
+
+def forwarder1(fp: FuncType[P], *args: P.args, **kw_args: P.kwargs) -> str:
+    return fp(0, '', *args, **kw_args)
+
+def forwarder2(fp: Callable[Concatenate[int, str, P], str], *args: P.args, **kw_args: P.kwargs) -> str:
+    return fp(0, '', *args, **kw_args)
+
+def my_f(x: int, s: str, d: bool) -> str: ...
+forwarder1(my_f, True)  # OK
+forwarder2(my_f, True)  # OK
+forwarder1(my_f, 1.0)  # E: Argument 2 to "forwarder1" has incompatible type "float"; expected "bool"
+forwarder2(my_f, 1.0)  # E: Argument 2 to "forwarder2" has incompatible type "float"; expected "bool"
+[builtins fixtures/paramspec.pyi]
+
+[case testParamSpecCallbackProtocolSelf]
+from typing import Callable, Protocol, TypeVar
+from typing_extensions import ParamSpec, Concatenate
+
+Params = ParamSpec("Params")
+Result = TypeVar("Result", covariant=True)
+
+class FancyMethod(Protocol):
+    def __call__(self, arg1: int, arg2: str) -> bool: ...
+    def return_me(self: Callable[Params, Result]) -> Callable[Params, Result]: ...
+    def return_part(self: Callable[Concatenate[int, Params], Result]) -> Callable[Params, Result]: ...
+
+m: FancyMethod
+reveal_type(m.return_me())  # N: Revealed type is "def (arg1: builtins.int, arg2: builtins.str) -> builtins.bool"
+reveal_type(m.return_part())  # N: Revealed type is "def (arg2: builtins.str) -> builtins.bool"
+[builtins fixtures/paramspec.pyi]
+
+[case testParamSpecInferenceCallableAgainstAny]
+from typing import Callable, TypeVar, Any
+from typing_extensions import ParamSpec, Concatenate
+
+_P = ParamSpec("_P")
+_R = TypeVar("_R")
+
+class A: ...
+a = A()
+
+def a_func(
+    func: Callable[Concatenate[A, _P], _R],
+) -> Callable[Concatenate[Any, _P], _R]:
+    def wrapper(__a: Any, *args: _P.args, **kwargs: _P.kwargs) -> _R:
+        return func(a, *args, **kwargs)
+    return wrapper
+
+def test(a, *args): ...
+x: Any
+y: object
+
+a_func(test)
+x = a_func(test)
+y = a_func(test)
+[builtins fixtures/paramspec.pyi]
+
 [case testParamSpecInferenceWithCallbackProtocol]
 from typing import Protocol, Callable, ParamSpec
 
diff --git a/test-data/unit/fixtures/paramspec.pyi b/test-data/unit/fixtures/paramspec.pyi
index 9b0089f6a7e9..dfb5e126f242 100644
--- a/test-data/unit/fixtures/paramspec.pyi
+++ b/test-data/unit/fixtures/paramspec.pyi
@@ -16,6 +16,7 @@ class object:
 
 class function: ...
 class ellipsis: ...
+class classmethod: ...
 
 class type:
     def __init__(self, *a: object) -> None: ...