diff --git a/masque/file/gdsii_lazy_core.py b/masque/file/gdsii_lazy_core.py
index f5dc994..bf4cde0 100644
--- a/masque/file/gdsii_lazy_core.py
+++ b/masque/file/gdsii_lazy_core.py
@@ -17,7 +17,7 @@ Both the classic and Arrow-backed lazy GDS readers rely on these helpers.
 from __future__ import annotations
 
 from dataclasses import dataclass
-from typing import IO, Any, cast
+from typing import IO, Any, Literal, cast
 from collections import defaultdict
 from collections.abc import Callable, Iterator, Mapping, Sequence
 import copy
@@ -303,7 +303,23 @@ class OverlayLibrary(ILibrary):
             source: Mapping[str, Pattern] | ILibraryView,
             *,
             rename_theirs: Callable[[ILibraryView, str], str] | None = None,
+            rename_when: Literal['conflict', 'always'] = 'conflict',
             ) -> dict[str, str]:
+        """
+        Add a source-backed library layer.
+
+        Args:
+            rename_theirs: Function used to choose visible names for imported
+                source cells.
+            rename_when: If `'conflict'`, only conflicting names are renamed.
+                If `'always'`, every imported source name is passed through
+                `rename_theirs`.
+        """
+        if rename_when not in ('conflict', 'always'):
+            raise ValueError(f'Unknown source rename mode: {rename_when!r}')
+        if rename_when == 'always' and rename_theirs is None:
+            raise TypeError('rename_theirs is required when rename_when="always"')
+
         view = _coerce_library_view(source)
         source_order = list(view.source_order())
         child_graph = view.child_graph(dangling='include')
@@ -314,12 +330,20 @@ class OverlayLibrary(ILibrary):
 
         for name in source_order:
             visible = name
-            if visible in self._entries or visible in visible_to_source:
+            renamed = False
+            if rename_when == 'always':
+                visible = cast('Callable[[ILibraryView, str], str]', rename_theirs)(self, name)
+                renamed = True
+            elif visible in self._entries or visible in visible_to_source:
                 if rename_theirs is None:
                     raise LibraryError(f'Conflicting name while adding source: {name!r}')
                 visible = rename_theirs(self, name)
-                if visible in self._entries or visible in visible_to_source:
-                    raise LibraryError(f'Unresolved duplicate key encountered while adding source: {name!r} -> {visible!r}')
+                renamed = True
+            if visible in self._entries or visible in visible_to_source:
+                if not renamed:
+                    raise LibraryError(f'Conflicting name while adding source: {name!r}')
+                raise LibraryError(f'Unresolved duplicate key encountered while adding source: {name!r} -> {visible!r}')
+            if visible != name:
                 rename_map[name] = visible
             source_to_visible[name] = visible
             visible_to_source[visible] = name
diff --git a/masque/test/test_gdsii_lazy.py b/masque/test/test_gdsii_lazy.py
index 6855783..0134d6e 100644
--- a/masque/test/test_gdsii_lazy.py
+++ b/masque/test/test_gdsii_lazy.py
@@ -1,6 +1,7 @@
 from pathlib import Path
 
 import numpy
+import pytest
 from numpy.testing import assert_allclose
 
 from ..file import gdsii, gdsii_lazy
@@ -82,6 +83,35 @@ def test_gdsii_lazy_overlay_add_source_stays_lazy_for_processed_view(tmp_path: P
     assert set(abstract.ports) == {'A'}
 
 
+def test_gdsii_lazy_overlay_add_source_can_rename_every_source_cell() -> None:
+    src = _make_lazy_port_library()
+    overlay = gdsii_lazy.OverlayLibrary()
+
+    rename_map = overlay.add_source(
+        src,
+        rename_theirs=lambda _lib, name: f'mapped_{name}',
+        rename_when='always',
+    )
+
+    assert rename_map == {
+        'leaf': 'mapped_leaf',
+        'child': 'mapped_child',
+        'top': 'mapped_top',
+    }
+    assert tuple(overlay.keys()) == ('mapped_leaf', 'mapped_child', 'mapped_top')
+    assert 'mapped_leaf' in overlay['mapped_child'].refs
+
+
+def test_gdsii_lazy_overlay_add_source_rename_when_validation() -> None:
+    src = _make_lazy_port_library()
+
+    with pytest.raises(TypeError, match='rename_theirs'):
+        gdsii_lazy.OverlayLibrary().add_source(src, rename_when='always')
+
+    with pytest.raises(ValueError, match='rename mode'):
+        gdsii_lazy.OverlayLibrary().add_source(src, rename_when='sometimes')   # type: ignore[arg-type]
+
+
 def test_gdsii_lazy_processed_write_roundtrips_without_explicit_units(tmp_path: Path) -> None:
     gds_file = tmp_path / 'lazy_roundtrip.gds'
     src = _make_lazy_port_library()