diff --git a/lib/matplotlib/_api/__init__.py b/lib/matplotlib/_api/__init__.py
index 97997cbe64f2..2e473c474526 100644
--- a/lib/matplotlib/_api/__init__.py
+++ b/lib/matplotlib/_api/__init__.py
@@ -189,6 +189,58 @@ def check_getitem(_mapping, **kwargs):
             .format(v, k, ', '.join(map(repr, mapping)))) from None
 
 
+def select_matching_signature(funcs, *args, **kwargs):
+    """
+    Select and call the function that accepts ``*args, **kwargs``.
+
+    *funcs* is a list of functions which should not raise any exception (other
+    than `TypeError` if the arguments passed do not match their signature).
+
+    `select_matching_signature` tries to call each of the functions in *funcs*
+    with ``*args, **kwargs`` (in the order in which they are given).  Calls
+    that fail with a `TypeError` are silently skipped.  As soon as a call
+    succeeds, `select_matching_signature` returns its return value.  If no
+    function accepts ``*args, **kwargs``, then the `TypeError` raised by the
+    last failing call is re-raised.
+
+    Callers should normally make sure that any ``*args, **kwargs`` can only
+    bind a single *func* (to avoid any ambiguity), although this is not checked
+    by `select_matching_signature`.
+
+    Notes
+    -----
+    `select_matching_signature` is intended to help implementing
+    signature-overloaded functions.  In general, such functions should be
+    avoided, except for back-compatibility concerns.  A typical use pattern is
+    ::
+
+        def my_func(*args, **kwargs):
+            params = select_matching_signature(
+                [lambda old1, old2: locals(), lambda new: locals()],
+                *args, **kwargs)
+            if "old1" in params:
+                warn_deprecated(...)
+                old1, old2 = params.values()  # note that locals() is ordered.
+            else:
+                new, = params.values()
+            # do things with params
+
+    which allows *my_func* to be called either with two parameters (*old1* and
+    *old2*) or a single one (*new*).  Note that the new signature is given
+    last, so that callers get a `TypeError` corresponding to the new signature
+    if the arguments they passed in do not match any signature.
+    """
+    # Rather than relying on locals() ordering, one could have just used func's
+    # signature (``bound = inspect.signature(func).bind(*args, **kwargs);
+    # bound.apply_defaults(); return bound``) but that is significantly slower.
+    for i, func in enumerate(funcs):
+        try:
+            return func(*args, **kwargs)
+        except TypeError:
+            if i == len(funcs) - 1:
+                raise
+
+
 def warn_external(message, category=None):
     """
     `warnings.warn` wrapper that sets *stacklevel* to "outside Matplotlib".
diff --git a/lib/matplotlib/collections.py b/lib/matplotlib/collections.py
index c2becd70733a..a0364d54e083 100644
--- a/lib/matplotlib/collections.py
+++ b/lib/matplotlib/collections.py
@@ -1994,32 +1994,23 @@ def __init__(self, *args, **kwargs):
         # signature deprecation since="3.5": Change to new signature after the
         # deprecation has expired. Also remove setting __init__.__signature__,
         # and remove the Notes from the docstring.
-        #
-        # We use lambdas to parse *args, **kwargs through the respective old
-        # and new signatures.
-        try:
-            # Old signature:
-            # The following raises a TypeError iif the args don't match.
-            w, h, coords, antialiased, shading, kwargs = (
+        params = _api.select_matching_signature(
+            [
                 lambda meshWidth, meshHeight, coordinates, antialiased=True,
-                       shading='flat', **kwargs:
-                (meshWidth, meshHeight, coordinates, antialiased, shading,
-                 kwargs))(*args, **kwargs)
-        except TypeError as exc:
-            # New signature:
-            # If the following raises a TypeError (i.e. args don't match),
-            # just let it propagate.
-            coords, antialiased, shading, kwargs = (
+                       shading='flat', **kwargs: locals(),
                 lambda coordinates, antialiased=True, shading='flat', **kwargs:
-                (coordinates, antialiased, shading, kwargs))(*args, **kwargs)
-            coords = np.asarray(coords, np.float64)
-        else:  # The old signature matched.
+                       locals()
+            ],
+            *args, **kwargs).values()
+        *old_w_h, coords, antialiased, shading, kwargs = params
+        if old_w_h:  # The old signature matched.
             _api.warn_deprecated(
                 "3.5",
                 message="This usage of Quadmesh is deprecated: Parameters "
                         "meshWidth and meshHeights will be removed; "
                         "coordinates must be 2D; all parameters except "
                         "coordinates will be keyword-only.")
+            w, h = old_w_h
             coords = np.asarray(coords, np.float64).reshape((h + 1, w + 1, 2))
         kwargs.setdefault("pickradius", 0)
         # end of signature deprecation code