diff --git a/CHANGES.rst b/CHANGES.rst
index 878dc024..0f49ffea 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -1,3 +1,9 @@
+v5.11.0
+=======
+
+* #265: ``MultiplexedPath`` now honors multiple subdirectories
+  in ``iterdir`` and ``joinpath``.
+
 v5.10.3
 =======
 
diff --git a/importlib_resources/_itertools.py b/importlib_resources/_itertools.py
index cce05582..7b775ef5 100644
--- a/importlib_resources/_itertools.py
+++ b/importlib_resources/_itertools.py
@@ -1,35 +1,38 @@
-from itertools import filterfalse
+# from more_itertools 9.0
+def only(iterable, default=None, too_long=None):
+    """If *iterable* has only one item, return it.
+    If it has zero items, return *default*.
+    If it has more than one item, raise the exception given by *too_long*,
+    which is ``ValueError`` by default.
+    >>> only([], default='missing')
+    'missing'
+    >>> only([1])
+    1
+    >>> only([1, 2])  # doctest: +IGNORE_EXCEPTION_DETAIL
+    Traceback (most recent call last):
+    ...
+    ValueError: Expected exactly one item in iterable, but got 1, 2,
+     and perhaps more.'
+    >>> only([1, 2], too_long=TypeError)  # doctest: +IGNORE_EXCEPTION_DETAIL
+    Traceback (most recent call last):
+    ...
+    TypeError
+    Note that :func:`only` attempts to advance *iterable* twice to ensure there
+    is only one item.  See :func:`spy` or :func:`peekable` to check
+    iterable contents less destructively.
+    """
+    it = iter(iterable)
+    first_value = next(it, default)
 
-from typing import (
-    Callable,
-    Iterable,
-    Iterator,
-    Optional,
-    Set,
-    TypeVar,
-    Union,
-)
-
-# Type and type variable definitions
-_T = TypeVar('_T')
-_U = TypeVar('_U')
-
-
-def unique_everseen(
-    iterable: Iterable[_T], key: Optional[Callable[[_T], _U]] = None
-) -> Iterator[_T]:
-    "List unique elements, preserving order. Remember all elements ever seen."
-    # unique_everseen('AAAABBBCCDAABBB') --> A B C D
-    # unique_everseen('ABBCcAD', str.lower) --> A B C D
-    seen: Set[Union[_T, _U]] = set()
-    seen_add = seen.add
-    if key is None:
-        for element in filterfalse(seen.__contains__, iterable):
-            seen_add(element)
-            yield element
+    try:
+        second_value = next(it)
+    except StopIteration:
+        pass
     else:
-        for element in iterable:
-            k = key(element)
-            if k not in seen:
-                seen_add(k)
-                yield element
+        msg = (
+            'Expected exactly one item in iterable, but got {!r}, {!r}, '
+            'and perhaps more.'.format(first_value, second_value)
+        )
+        raise too_long or ValueError(msg)
+
+    return first_value
diff --git a/importlib_resources/readers.py b/importlib_resources/readers.py
index c5d435f4..51d030a6 100644
--- a/importlib_resources/readers.py
+++ b/importlib_resources/readers.py
@@ -1,10 +1,11 @@
 import collections
+import itertools
 import pathlib
 import operator
 
 from . import abc
 
-from ._itertools import unique_everseen
+from ._itertools import only
 from ._compat import ZipPath
 
 
@@ -69,8 +70,10 @@ def __init__(self, *paths):
             raise NotADirectoryError('MultiplexedPath only supports directories')
 
     def iterdir(self):
-        files = (file for path in self._paths for file in path.iterdir())
-        return unique_everseen(files, key=operator.attrgetter('name'))
+        children = (child for path in self._paths for child in path.iterdir())
+        by_name = operator.attrgetter('name')
+        groups = itertools.groupby(sorted(children, key=by_name), key=by_name)
+        return map(self._follow, (locs for name, locs in groups))
 
     def read_bytes(self):
         raise FileNotFoundError(f'{self} is not a file')
@@ -92,6 +95,25 @@ def joinpath(self, *descendants):
             # Just return something that will not exist.
             return self._paths[0].joinpath(*descendants)
 
+    @classmethod
+    def _follow(cls, children):
+        """
+        Construct a MultiplexedPath if needed.
+
+        If children contains a sole element, return it.
+        Otherwise, return a MultiplexedPath of the items.
+        Unless one of the items is not a Directory, then return the first.
+        """
+        subdirs, one_dir, one_file = itertools.tee(children, 3)
+
+        try:
+            return only(one_dir)
+        except ValueError:
+            try:
+                return cls(*subdirs)
+            except NotADirectoryError:
+                return next(one_file)
+
     def open(self, *args, **kwargs):
         raise FileNotFoundError(f'{self} is not a file')
 
diff --git a/importlib_resources/tests/data02/subdirectory/subsubdir/resource.txt b/importlib_resources/tests/data02/subdirectory/subsubdir/resource.txt
new file mode 100644
index 00000000..48f587a2
--- /dev/null
+++ b/importlib_resources/tests/data02/subdirectory/subsubdir/resource.txt
@@ -0,0 +1 @@
+a resource
\ No newline at end of file
diff --git a/importlib_resources/tests/test_reader.py b/importlib_resources/tests/test_reader.py
index 1c8ebeeb..e2bdf19c 100644
--- a/importlib_resources/tests/test_reader.py
+++ b/importlib_resources/tests/test_reader.py
@@ -81,6 +81,17 @@ def test_join_path_compound(self):
         path = MultiplexedPath(self.folder)
         assert not path.joinpath('imaginary/foo.py').exists()
 
+    def test_join_path_common_subdir(self):
+        prefix = os.path.abspath(os.path.join(__file__, '..'))
+        data01 = os.path.join(prefix, 'data01')
+        data02 = os.path.join(prefix, 'data02')
+        path = MultiplexedPath(data01, data02)
+        self.assertIsInstance(path.joinpath('subdirectory'), MultiplexedPath)
+        self.assertEqual(
+            str(path.joinpath('subdirectory', 'subsubdir'))[len(prefix) + 1 :],
+            os.path.join('data02', 'subdirectory', 'subsubdir'),
+        )
+
     def test_repr(self):
         self.assertEqual(
             repr(MultiplexedPath(self.folder)),