diff --git a/src/pdm/backend/wheel.py b/src/pdm/backend/wheel.py
index 7828ffd..0c38eec 100644
--- a/src/pdm/backend/wheel.py
+++ b/src/pdm/backend/wheel.py
@@ -81,7 +81,9 @@ def scheme_path(self, name: str, relative: str) -> str:
             )
         return f"{self.name_version}.data/{name}/{relative}"
 
-    def _get_platform_tags(self) -> tuple[str | None, str | None, str | None]:
+    def _get_platform_tags(
+        self,
+    ) -> tuple[str | None, str | None, list[str] | str | None]:
         python_tag: str | None = None
         py_limited_api: str | None = None
         plat_name: str | None = None
@@ -219,9 +221,14 @@ def _get_tag(self) -> str:
                 else:
                     impl = "py3"
 
-        platform = platform.lower().replace("-", "_").replace(".", "_")  # type: ignore
+        if isinstance(platform, str):
+            platform = [platform]
+
+        platform = ".".join(
+            x.lower().replace("-", "_").replace(".", "_") for x in platform
+        )
         tag = (impl, abi, platform)
-        return "-".join(tag)  # type: ignore[arg-type]
+        return "-".join(tag)
 
     def _write_dist_info(self, parent: Path) -> Path:
         """write the dist-info directory and return the path to it"""
diff --git a/tests/test_wheel.py b/tests/test_wheel.py
index 9ad6907..f10cf7d 100644
--- a/tests/test_wheel.py
+++ b/tests/test_wheel.py
@@ -1,3 +1,5 @@
+from __future__ import annotations
+
 import sys
 from pathlib import Path
 
@@ -13,10 +15,16 @@
     [
         ("cp36", "abi3", "win_amd64", "cp36-abi3-win_amd64"),
         ("py3", "none", "win_amd64", "py3-none-win_amd64"),
+        (
+            "py3",
+            "none",
+            ["manylinux_2_12_x86", "musllinux_1_1_x86"],
+            "py3-none-manylinux_2_12_x86.musllinux_1_1_x86",
+        ),
     ],
 )
 def test_override_tags_in_wheel_filename(
-    python_tag: str, py_limited_api: str, plat_name: str, tag: str
+    python_tag: str, py_limited_api: str, plat_name: str | list[str], tag: str
 ) -> None:
     project = FIXTURES / "projects/demo-cextension"
     with wheel.WheelBuilder(