diff --git a/stdlib/@tests/test_cases/builtins/check_exception_group-py311.py b/stdlib/@tests/test_cases/builtins/check_exception_group-py311.py
index b1bf701c4b8c..8d8ea0cbebed 100644
--- a/stdlib/@tests/test_cases/builtins/check_exception_group-py311.py
+++ b/stdlib/@tests/test_cases/builtins/check_exception_group-py311.py
@@ -2,7 +2,7 @@
 
 import sys
 from typing import TypeVar
-from typing_extensions import assert_type
+from typing_extensions import Never, assert_type
 
 if sys.version_info >= (3, 11):
     # This can be removed later, but right now Flake8 does not know
@@ -21,9 +21,7 @@
 
     # `BaseExceptionGroup` can work with `Exception`:
     beg2 = BaseExceptionGroup("x", [ValueError()])
-    # FIXME: this is not right, runtime returns `ExceptionGroup` instance instead,
-    # but I am unable to represent this with types right now.
-    assert_type(beg2, BaseExceptionGroup[ValueError])
+    assert_type(beg2, ExceptionGroup[ValueError])
 
     # .subgroup()
     # -----------
@@ -218,7 +216,13 @@ class CustomBaseGroup(BaseExceptionGroup[_BE]): ...
 
     cb1 = CustomBaseGroup("x", [SystemExit()])
     assert_type(cb1, CustomBaseGroup[SystemExit])
-    cb2 = CustomBaseGroup("x", [ValueError()])
+
+    # Custom subclasses that don't implement __new__ are now kinda borked when
+    # passing non-base exceptions.
+    # With current typing it's not possible to have this working at the same time
+    # as making BaseExceptionGroup initialized with non-base exceptions return ExceptionGroup
+    assert_type(CustomBaseGroup("x", [ValueError()]), CustomBaseGroup[Never])
+    cb2: CustomBaseGroup[ValueError] = CustomBaseGroup("x", [ValueError()])
     assert_type(cb2, CustomBaseGroup[ValueError])
 
     # .subgroup()
diff --git a/stdlib/builtins.pyi b/stdlib/builtins.pyi
index 0a6dc57b05b8..cfb6353cbe00 100644
--- a/stdlib/builtins.pyi
+++ b/stdlib/builtins.pyi
@@ -2076,8 +2076,13 @@ if sys.version_info >= (3, 11):
 
     # See `check_exception_group.py` for use-cases and comments.
     class BaseExceptionGroup(BaseException, Generic[_BaseExceptionT_co]):
+        @overload
+        # mypy thinks this is an invalid type for cls/self
+        def __new__(  # type: ignore[misc]
+            cls: ExceptionGroup[_ExceptionT_co], message: str, exceptions: Sequence[_ExceptionT_co], /
+        ) -> ExceptionGroup[_ExceptionT_co]: ...
+        @overload
         def __new__(cls, message: str, exceptions: Sequence[_BaseExceptionT_co], /) -> Self: ...
-        def __init__(self, message: str, exceptions: Sequence[_BaseExceptionT_co], /) -> None: ...
         @property
         def message(self) -> str: ...
         @property