diff --git a/lib/matplotlib/tests/test_transforms.py b/lib/matplotlib/tests/test_transforms.py
index d869240adaec..3af9af68ec94 100644
--- a/lib/matplotlib/tests/test_transforms.py
+++ b/lib/matplotlib/tests/test_transforms.py
@@ -700,6 +700,18 @@ def test_contains_branch(self):
         assert x is sx is False
         assert y is sy is True
 
+        # A branch that lives in the first child of a composite, or that spans
+        # the boundary between its two children, must be reported in both
+        # dimensions, consistently with contains_branch (issue #32099).
+        assert self.stack2.contains_branch(self.stack2_subset)
+        assert (self.stack2.contains_branch_separately(self.stack2_subset)
+                == (True, True))
+        assert (self.stack1.contains_branch_separately(self.ta2 + self.ta3)
+                == (True, True))
+        # A transform that is not a branch stays False in both dimensions.
+        assert (self.stack2.contains_branch_separately(self.tn1)
+                == (False, False))
+
     def test_affine_simplification(self):
         # tests that a transform stack only calls as much is absolutely
         # necessary "non-affine" allowing the best possible optimization with
diff --git a/lib/matplotlib/transforms.py b/lib/matplotlib/transforms.py
index 2b46deae43dd..d61fefa2b221 100644
--- a/lib/matplotlib/transforms.py
+++ b/lib/matplotlib/transforms.py
@@ -2454,7 +2454,18 @@ def contains_branch_separately(self, other_transform):
                              'transforms with 2 output dimensions')
         if self == other_transform:
             return (True, True)
-        return self._b.contains_branch_separately(other_transform)
+        # The second (suffix) child may report per-dimension results when it
+        # is a blended transform, so query it separately first.
+        x, y = self._b.contains_branch_separately(other_transform)
+        if not (x and y):
+            # Otherwise the branch may lie in the first child or span the
+            # boundary between the two children.  Such a branch is a suffix of
+            # the whole composite and therefore matches in both dimensions, so
+            # fall back to the (non-per-dimension) whole-transform check.
+            in_branch = self.contains_branch(other_transform)
+            x = x or in_branch
+            y = y or in_branch
+        return (x, y)
 
     depth = property(lambda self: self._a.depth + self._b.depth)
     is_affine = property(lambda self: self._a.is_affine and self._b.is_affine)