diff --git a/changes/3777-PrettyWood.md b/changes/3777-PrettyWood.md
new file mode 100644
index 0000000..97475e0
--- /dev/null
+++ b/changes/3777-PrettyWood.md
@@ -0,0 +1 @@
+support overwriting dunder attributes of `BaseModel` instances
diff --git a/pydantic/main.py b/pydantic/main.py
index 4b8daec..8c0e9f8 100644
--- a/pydantic/main.py
+++ b/pydantic/main.py
@@ -53,6 +53,7 @@ from .typing import (
     update_model_forward_refs,
 )
 from .utils import (
+    DUNDER_ATTRIBUTES,
     ROOT_KEY,
     ClassAttribute,
     GetterDict,
@@ -350,7 +351,7 @@ class BaseModel(Representation, metaclass=ModelMetaclass):
 
     @no_type_check
     def __setattr__(self, name, value):  # noqa: C901 (ignore complexity)
-        if name in self.__private_attributes__:
+        if name in self.__private_attributes__ or name in DUNDER_ATTRIBUTES:
             return object_setattr(self, name, value)
 
         if self.__config__.extra is not Extra.allow and name not in self.__fields__:
@@ -891,7 +892,9 @@ class BaseModel(Representation, metaclass=ModelMetaclass):
 
     def __repr_args__(self) -> 'ReprArgs':
         return [
-            (k, v) for k, v in self.__dict__.items() if k not in self.__fields__ or self.__fields__[k].field_info.repr
+            (k, v)
+            for k, v in self.__dict__.items()
+            if k not in DUNDER_ATTRIBUTES and (k not in self.__fields__ or self.__fields__[k].field_info.repr)
         ]
 
 
diff --git a/pydantic/utils.py b/pydantic/utils.py
index ffec554..51c0253 100644
--- a/pydantic/utils.py
+++ b/pydantic/utils.py
@@ -78,6 +78,7 @@ __all__ = (
     'ROOT_KEY',
     'get_unique_discriminator_alias',
     'get_discriminator_alias_and_values',
+    'DUNDER_ATTRIBUTES',
     'LimitedDict',
 )
 
@@ -691,15 +692,19 @@ def is_valid_field(name: str) -> bool:
     return ROOT_KEY == name
 
 
+DUNDER_ATTRIBUTES = {
+    '__annotations__',
+    '__classcell__',
+    '__doc__',
+    '__module__',
+    '__orig_bases__',
+    '__orig_class__',
+    '__qualname__',
+}
+
+
 def is_valid_private_name(name: str) -> bool:
-    return not is_valid_field(name) and name not in {
-        '__annotations__',
-        '__classcell__',
-        '__doc__',
-        '__module__',
-        '__orig_bases__',
-        '__qualname__',
-    }
+    return not is_valid_field(name) and name not in DUNDER_ATTRIBUTES
 
 
 _EMPTY = object()
diff --git a/tests/test_main.py b/tests/test_main.py
index ceac222..16faaba 100644
--- a/tests/test_main.py
+++ b/tests/test_main.py
@@ -19,6 +19,7 @@ from typing import (
 from uuid import UUID, uuid4
 
 import pytest
+from typing_extensions import Annotated
 
 from pydantic import (
     BaseConfig,
@@ -2174,6 +2175,19 @@ def test_new_union_origin():
     }
 
 
+def test_annotated_class():
+    class PydanticModel(BaseModel):
+        foo: str = '123'
+
+    PydanticAlias = Annotated[PydanticModel, 'bar baz']
+
+    pa = PydanticAlias()
+    assert isinstance(pa, PydanticModel)
+    pa.__doc__ = 'qwe'
+    assert repr(pa) == "PydanticModel(foo='123')"
+    assert pa.__doc__ == 'qwe'
+
+
 @pytest.mark.parametrize(
     'ann',
     [Final, Final[int]],