diff --git a/lib/matplotlib/path.py b/lib/matplotlib/path.py
index 3fa3fb262e27..aef2e9044c6a 100644
--- a/lib/matplotlib/path.py
+++ b/lib/matplotlib/path.py
@@ -276,17 +276,37 @@ def copy(self):
         """
         return copy.copy(self)
 
-    def __deepcopy__(self, memo=None):
+    def __deepcopy__(self, memo):
         """
         Return a deepcopy of the `Path`.  The `Path` will not be
         readonly, even if the source `Path` is.
         """
         # Deepcopying arrays (vertices, codes) strips the writeable=False flag.
-        p = copy.deepcopy(super(), memo)
+        cls = type(self)
+        memo[id(self)] = p = cls.__new__(cls)
+
+        for k, v in self.__dict__.items():
+            setattr(p, k, copy.deepcopy(v, memo))
+
         p._readonly = False
         return p
 
-    deepcopy = __deepcopy__
+    def deepcopy(self, memo=None):
+        """
+        Return a deep copy of the `Path`.  The `Path` will not be readonly,
+        even if the source `Path` is.
+
+        Parameters
+        ----------
+        memo : dict, optional
+            A dictionary to use for memoizing, passed to `copy.deepcopy`.
+
+        Returns
+        -------
+        Path
+            A deep copy of the `Path`, but not readonly.
+        """
+        return copy.deepcopy(self, memo)
 
     @classmethod
     def make_compound_path_from_polys(cls, XY):
diff --git a/lib/matplotlib/path.pyi b/lib/matplotlib/path.pyi
index 464fc6d9a912..8a5a5c03792e 100644
--- a/lib/matplotlib/path.pyi
+++ b/lib/matplotlib/path.pyi
@@ -44,8 +44,8 @@ class Path:
     @property
     def readonly(self) -> bool: ...
     def copy(self) -> Path: ...
-    def __deepcopy__(self, memo: dict[int, Any] | None = ...) -> Path: ...
-    deepcopy = __deepcopy__
+    def __deepcopy__(self, memo: dict[int, Any]) -> Path: ...
+    def deepcopy(self, memo: dict[int, Any] | None = None) -> Path: ...
 
     @classmethod
     def make_compound_path_from_polys(cls, XY: ArrayLike) -> Path: ...
diff --git a/lib/matplotlib/tests/test_path.py b/lib/matplotlib/tests/test_path.py
index 21f4c33794af..1ec6209bbbb4 100644
--- a/lib/matplotlib/tests/test_path.py
+++ b/lib/matplotlib/tests/test_path.py
@@ -355,15 +355,49 @@ def test_path_deepcopy():
     # Should not raise any error
     verts = [[0, 0], [1, 1]]
     codes = [Path.MOVETO, Path.LINETO]
-    path1 = Path(verts)
-    path2 = Path(verts, codes)
+    path1 = Path(verts, readonly=True)
+    path2 = Path(verts, codes, readonly=True)
     path1_copy = path1.deepcopy()
     path2_copy = path2.deepcopy()
     assert path1 is not path1_copy
     assert path1.vertices is not path1_copy.vertices
+    assert_array_equal(path1.vertices, path1_copy.vertices)
+    assert path1.readonly
+    assert not path1_copy.readonly
     assert path2 is not path2_copy
     assert path2.vertices is not path2_copy.vertices
+    assert_array_equal(path2.vertices, path2_copy.vertices)
     assert path2.codes is not path2_copy.codes
+    assert_array_equal(path2.codes, path2_copy.codes)
+    assert path2.readonly
+    assert not path2_copy.readonly
+
+
+def test_path_deepcopy_cycle():
+    class PathWithCycle(Path):
+        def __init__(self, *args, **kwargs):
+            super().__init__(*args, **kwargs)
+            self.x = self
+
+    p = PathWithCycle([[0, 0], [1, 1]], readonly=True)
+    p_copy = p.deepcopy()
+    assert p_copy is not p
+    assert p.readonly
+    assert not p_copy.readonly
+    assert p_copy.x is p_copy
+
+    class PathWithCycle2(Path):
+        def __init__(self, *args, **kwargs):
+            super().__init__(*args, **kwargs)
+            self.x = [self] * 2
+
+    p2 = PathWithCycle2([[0, 0], [1, 1]], readonly=True)
+    p2_copy = p2.deepcopy()
+    assert p2_copy is not p2
+    assert p2.readonly
+    assert not p2_copy.readonly
+    assert p2_copy.x[0] is p2_copy
+    assert p2_copy.x[1] is p2_copy
 
 
 def test_path_shallowcopy():
diff --git a/lib/matplotlib/transforms.py b/lib/matplotlib/transforms.py
index 2934b0a77809..ca04e729df4f 100644
--- a/lib/matplotlib/transforms.py
+++ b/lib/matplotlib/transforms.py
@@ -35,7 +35,6 @@
 # `np.minimum` instead of the builtin `min`, and likewise for `max`.  This is
 # done so that `nan`s are propagated, instead of being silently dropped.
 
-import copy
 import functools
 import itertools
 import textwrap
@@ -141,7 +140,9 @@ def __setstate__(self, data_dict):
             for k, v in self._parents.items() if v is not None}
 
     def __copy__(self):
-        other = copy.copy(super())
+        cls = type(self)
+        other = cls.__new__(cls)
+        other.__dict__.update(self.__dict__)
         # If `c = a + b; a1 = copy(a)`, then modifications to `a1` do not
         # propagate back to `c`, i.e. we need to clear the parents of `a1`.
         other._parents = {}