diff --git a/mypy/checker.py b/mypy/checker.py
index c7de4911501a..7a66a9408ee4 100644
--- a/mypy/checker.py
+++ b/mypy/checker.py
@@ -184,7 +184,6 @@
     LiteralType,
     NoneType,
     Overloaded,
-    ParamSpecType,
     PartialType,
     ProperType,
     StarType,
@@ -203,7 +202,6 @@
     UnboundType,
     UninhabitedType,
     UnionType,
-    UnpackType,
     flatten_nested_unions,
     get_proper_type,
     get_proper_types,
@@ -211,6 +209,7 @@
     is_named_instance,
     is_optional,
     remove_optional,
+    store_argument_type,
     strip_type,
 )
 from mypy.typetraverser import TypeTraverserVisitor
@@ -1174,30 +1173,8 @@ def check_func_def(
                             if ctx.line < 0:
                                 ctx = typ
                             self.fail(message_registry.FUNCTION_PARAMETER_CANNOT_BE_COVARIANT, ctx)
-                    if typ.arg_kinds[i] == nodes.ARG_STAR:
-                        if isinstance(arg_type, ParamSpecType):
-                            pass
-                        elif isinstance(arg_type, UnpackType):
-                            if isinstance(get_proper_type(arg_type.type), TupleType):
-                                # Instead of using Tuple[Unpack[Tuple[...]]], just use
-                                # Tuple[...]
-                                arg_type = arg_type.type
-                            else:
-                                arg_type = TupleType(
-                                    [arg_type],
-                                    fallback=self.named_generic_type(
-                                        "builtins.tuple", [self.named_type("builtins.object")]
-                                    ),
-                                )
-                        else:
-                            # builtins.tuple[T] is typing.Tuple[T, ...]
-                            arg_type = self.named_generic_type("builtins.tuple", [arg_type])
-                    elif typ.arg_kinds[i] == nodes.ARG_STAR2:
-                        if not isinstance(arg_type, ParamSpecType) and not typ.unpack_kwargs:
-                            arg_type = self.named_generic_type(
-                                "builtins.dict", [self.str_type(), arg_type]
-                            )
-                    item.arguments[i].variable.type = arg_type
+                    # Need to store arguments again for the expanded item.
+                    store_argument_type(item, i, typ, self.named_generic_type)
 
                 # Type check initialization expressions.
                 body_is_trivial = is_trivial_body(defn.body)
diff --git a/mypy/semanal.py b/mypy/semanal.py
index 538e37c030a9..a5ddcc70eed6 100644
--- a/mypy/semanal.py
+++ b/mypy/semanal.py
@@ -273,6 +273,7 @@
     get_proper_types,
     invalid_recursive_alias,
     is_named_instance,
+    store_argument_type,
 )
 from mypy.typevars import fill_typevars
 from mypy.util import (
@@ -1315,7 +1316,10 @@ def analyze_function_body(self, defn: FuncItem) -> None:
             # Bind the type variables again to visit the body.
             if defn.type:
                 a = self.type_analyzer()
-                a.bind_function_type_variables(cast(CallableType, defn.type), defn)
+                typ = cast(CallableType, defn.type)
+                a.bind_function_type_variables(typ, defn)
+                for i in range(len(typ.arg_types)):
+                    store_argument_type(defn, i, typ, self.named_type)
             self.function_stack.append(defn)
             with self.enter(defn):
                 for arg in defn.arguments:
@@ -2018,7 +2022,9 @@ def analyze_base_classes(
                 continue
 
             try:
-                base = self.expr_to_analyzed_type(base_expr, allow_placeholder=True)
+                base = self.expr_to_analyzed_type(
+                    base_expr, allow_placeholder=True, allow_type_any=True
+                )
             except TypeTranslationError:
                 name = self.get_name_repr_of_expr(base_expr)
                 if isinstance(base_expr, CallExpr):
@@ -6139,7 +6145,11 @@ def accept(self, node: Node) -> None:
             report_internal_error(err, self.errors.file, node.line, self.errors, self.options)
 
     def expr_to_analyzed_type(
-        self, expr: Expression, report_invalid_types: bool = True, allow_placeholder: bool = False
+        self,
+        expr: Expression,
+        report_invalid_types: bool = True,
+        allow_placeholder: bool = False,
+        allow_type_any: bool = False,
     ) -> Type | None:
         if isinstance(expr, CallExpr):
             # This is a legacy syntax intended mostly for Python 2, we keep it for
@@ -6164,7 +6174,10 @@ def expr_to_analyzed_type(
             return TupleType(info.tuple_type.items, fallback=fallback)
         typ = self.expr_to_unanalyzed_type(expr)
         return self.anal_type(
-            typ, report_invalid_types=report_invalid_types, allow_placeholder=allow_placeholder
+            typ,
+            report_invalid_types=report_invalid_types,
+            allow_placeholder=allow_placeholder,
+            allow_type_any=allow_type_any,
         )
 
     def analyze_type_expr(self, expr: Expression) -> None:
@@ -6188,6 +6201,7 @@ def type_analyzer(
         allow_param_spec_literals: bool = False,
         report_invalid_types: bool = True,
         prohibit_self_type: str | None = None,
+        allow_type_any: bool = False,
     ) -> TypeAnalyser:
         if tvar_scope is None:
             tvar_scope = self.tvar_scope
@@ -6204,6 +6218,7 @@ def type_analyzer(
             allow_required=allow_required,
             allow_param_spec_literals=allow_param_spec_literals,
             prohibit_self_type=prohibit_self_type,
+            allow_type_any=allow_type_any,
         )
         tpan.in_dynamic_func = bool(self.function_stack and self.function_stack[-1].is_dynamic())
         tpan.global_scope = not self.type and not self.function_stack
@@ -6224,6 +6239,7 @@ def anal_type(
         allow_param_spec_literals: bool = False,
         report_invalid_types: bool = True,
         prohibit_self_type: str | None = None,
+        allow_type_any: bool = False,
         third_pass: bool = False,
     ) -> Type | None:
         """Semantically analyze a type.
@@ -6260,6 +6276,7 @@ def anal_type(
             allow_param_spec_literals=allow_param_spec_literals,
             report_invalid_types=report_invalid_types,
             prohibit_self_type=prohibit_self_type,
+            allow_type_any=allow_type_any,
         )
         tag = self.track_incomplete_refs()
         typ = typ.accept(a)
diff --git a/mypy/stubtest.py b/mypy/stubtest.py
index 87ccbd3176df..74e57d9e5617 100644
--- a/mypy/stubtest.py
+++ b/mypy/stubtest.py
@@ -354,7 +354,7 @@ def _verify_final(
 ) -> Iterator[Error]:
     try:
 
-        class SubClass(runtime):  # type: ignore[misc,valid-type]
+        class SubClass(runtime):  # type: ignore[misc]
             pass
 
     except TypeError:
diff --git a/mypy/treetransform.py b/mypy/treetransform.py
index c863db6b3dd5..2f678b89b1e6 100644
--- a/mypy/treetransform.py
+++ b/mypy/treetransform.py
@@ -550,7 +550,7 @@ def visit_super_expr(self, node: SuperExpr) -> SuperExpr:
         return new
 
     def visit_assignment_expr(self, node: AssignmentExpr) -> AssignmentExpr:
-        return AssignmentExpr(node.target, node.value)
+        return AssignmentExpr(self.expr(node.target), self.expr(node.value))
 
     def visit_unary_expr(self, node: UnaryExpr) -> UnaryExpr:
         new = UnaryExpr(node.op, self.expr(node.expr))
diff --git a/mypy/typeanal.py b/mypy/typeanal.py
index 18a63011c5bf..fc84744c8cea 100644
--- a/mypy/typeanal.py
+++ b/mypy/typeanal.py
@@ -201,6 +201,7 @@ def __init__(
         allow_param_spec_literals: bool = False,
         report_invalid_types: bool = True,
         prohibit_self_type: str | None = None,
+        allow_type_any: bool = False,
     ) -> None:
         self.api = api
         self.lookup_qualified = api.lookup_qualified
@@ -237,6 +238,8 @@ def __init__(
         # Names of type aliases encountered while analysing a type will be collected here.
         self.aliases_used: set[str] = set()
         self.prohibit_self_type = prohibit_self_type
+        # Allow variables typed as Type[Any] and type (useful for base classes).
+        self.allow_type_any = allow_type_any
 
     def visit_unbound_type(self, t: UnboundType, defining_literal: bool = False) -> Type:
         typ = self.visit_unbound_type_nonoptional(t, defining_literal)
@@ -730,6 +733,11 @@ def analyze_unbound_type_without_type_info(
                 return AnyType(
                     TypeOfAny.from_unimported_type, missing_import_name=typ.missing_import_name
                 )
+            elif self.allow_type_any:
+                if isinstance(typ, Instance) and typ.type.fullname == "builtins.type":
+                    return AnyType(TypeOfAny.special_form)
+                if isinstance(typ, TypeType) and isinstance(typ.item, AnyType):
+                    return AnyType(TypeOfAny.from_another_any, source_any=typ.item)
         # Option 2:
         # Unbound type variable. Currently these may be still valid,
         # for example when defining a generic type alias.
diff --git a/mypy/types.py b/mypy/types.py
index 1de294f9952d..2ce38add63d0 100644
--- a/mypy/types.py
+++ b/mypy/types.py
@@ -7,6 +7,7 @@
 from typing import (
     TYPE_CHECKING,
     Any,
+    Callable,
     ClassVar,
     Dict,
     Iterable,
@@ -29,6 +30,7 @@
     ArgKind,
     FakeInfo,
     FuncDef,
+    FuncItem,
     SymbolNode,
 )
 from mypy.state import state
@@ -3390,3 +3392,29 @@ def callable_with_ellipsis(any_type: AnyType, ret_type: Type, fallback: Instance
         fallback=fallback,
         is_ellipsis_args=True,
     )
+
+
+def store_argument_type(
+    defn: FuncItem, i: int, typ: CallableType, named_type: Callable[[str, list[Type]], Instance]
+) -> None:
+    arg_type = typ.arg_types[i]
+    if typ.arg_kinds[i] == ARG_STAR:
+        if isinstance(arg_type, ParamSpecType):
+            pass
+        elif isinstance(arg_type, UnpackType):
+            if isinstance(get_proper_type(arg_type.type), TupleType):
+                # Instead of using Tuple[Unpack[Tuple[...]]], just use
+                # Tuple[...]
+                arg_type = arg_type.type
+            else:
+                arg_type = TupleType(
+                    [arg_type],
+                    fallback=named_type("builtins.tuple", [named_type("builtins.object", [])]),
+                )
+        else:
+            # builtins.tuple[T] is typing.Tuple[T, ...]
+            arg_type = named_type("builtins.tuple", [arg_type])
+    elif typ.arg_kinds[i] == ARG_STAR2:
+        if not isinstance(arg_type, ParamSpecType) and not typ.unpack_kwargs:
+            arg_type = named_type("builtins.dict", [named_type("builtins.str", []), arg_type])
+    defn.arguments[i].variable.type = arg_type
diff --git a/test-data/unit/check-classes.test b/test-data/unit/check-classes.test
index 33208c081c28..e3aea122ebe1 100644
--- a/test-data/unit/check-classes.test
+++ b/test-data/unit/check-classes.test
@@ -7664,3 +7664,18 @@ class C(B):
     def foo(self) -> int:  # E: Signature of "foo" incompatible with supertype "B"
         ...
 [builtins fixtures/property.pyi]
+
+[case testAllowArgumentAsBaseClass]
+from typing import Any, Type
+
+def e(b) -> None:
+    class D(b): ...
+
+def f(b: Any) -> None:
+    class D(b): ...
+
+def g(b: Type[Any]) -> None:
+    class D(b): ...
+
+def h(b: type) -> None:
+    class D(b): ...
diff --git a/test-data/unit/check-python38.test b/test-data/unit/check-python38.test
index 1922192c2877..30bdadf900c3 100644
--- a/test-data/unit/check-python38.test
+++ b/test-data/unit/check-python38.test
@@ -718,3 +718,19 @@ def f1() -> None:
         y = x
     z = x
 [builtins fixtures/dict.pyi]
+
+[case testNarrowOnSelfInGeneric]
+# flags: --strict-optional
+from typing import Generic, TypeVar, Optional
+
+T = TypeVar("T", int, str)
+
+class C(Generic[T]):
+    x: Optional[T]
+    def meth(self) -> Optional[T]:
+        if (y := self.x) is not None:
+            reveal_type(y)
+        return None
+[out]
+main:10: note: Revealed type is "builtins.int"
+main:10: note: Revealed type is "builtins.str"
diff --git a/test-data/unit/check-selftype.test b/test-data/unit/check-selftype.test
index 494ae54400fb..b002746a3397 100644
--- a/test-data/unit/check-selftype.test
+++ b/test-data/unit/check-selftype.test
@@ -1772,3 +1772,16 @@ class D(C): ...
 
 reveal_type(D.f)  # N: Revealed type is "def [T] (T`-1) -> T`-1"
 reveal_type(D().f)  # N: Revealed type is "def () -> __main__.D"
+
+[case testTypingSelfOnSuperTypeVarValues]
+from typing import Self, Generic, TypeVar
+
+T = TypeVar("T", int, str)
+
+class B:
+    def copy(self) -> Self: ...
+class C(B, Generic[T]):
+    def copy(self) -> Self:
+        inst = super().copy()
+        reveal_type(inst)  # N: Revealed type is "Self`0"
+        return inst
diff --git a/test-data/unit/semanal-types.test b/test-data/unit/semanal-types.test
index d832772f5f81..8dc767e1abfc 100644
--- a/test-data/unit/semanal-types.test
+++ b/test-data/unit/semanal-types.test
@@ -790,6 +790,7 @@ def f(x: int) -> None: pass
 def f(*args) -> None: pass
 
 x = f
+[builtins fixtures/tuple.pyi]
 [out]
 MypyFile:1(
   ImportFrom:1(typing, [overload])
@@ -1032,6 +1033,7 @@ MypyFile:1(
 
 [case testVarArgsAndKeywordArgs]
 def g(*x: int, y: str = ''): pass
+[builtins fixtures/tuple.pyi]
 [out]
 MypyFile:1(
   FuncDef:1(