diff --git a/crossenv/__init__.py b/crossenv/__init__.py
index b1119f1..5cd68bc 100644
--- a/crossenv/__init__.py
+++ b/crossenv/__init__.py
@@ -616,6 +616,10 @@ def get_uname_info(self):
             "EXT_SUFFIX"
         ]
 
+        self.sysconfig_extension_suffixes = (
+            [self.sysconfig_ext_suffix] + self._host_abi3_suffixes() + [".so"]
+        )
+
         # Normalize case of the host system/sysname.
         self.host_system = {
             "ios": "iOS",
@@ -631,6 +635,47 @@ def get_uname_info(self):
             "watchos": "Darwin",
         }.get(self.host_sys_platform, self.host_sys_platform.title())
 
+    def _host_soabi_platform(self):
+        """
+        SOABI_PLATFORM from the host's EXT_SUFFIX, or "" if absent.
+
+        EXT_SUFFIX is "." + SOABI + ".so", and SOABI is
+        "cpython-<ver>[-<PLATFORM_TRIPLET>]". CPython only emits the
+        platform-tagged abi3 suffixes when that triplet is defined.
+        """
+        ext_suffix = self.sysconfig_ext_suffix
+        if not ext_suffix.startswith(".") or not ext_suffix.endswith(".so"):
+            return ""
+        return "-".join(ext_suffix[1:-3].split("-")[2:])
+
+    def _host_abi3_suffixes(self):
+        """
+        Stable-ABI suffixes the HOST interpreter can load.
+
+        CPython builds these in Python/dynload_shlib.c. The plain ".abi3"
+        entries sit inside an "#ifndef Py_GIL_DISABLED" block, and both the
+        platform-tagged forms and the ".abi3t" forms only exist from 3.15.
+        """
+        free_threaded = self.host_sysconfigdata.build_time_vars.get("Py_GIL_DISABLED")
+        try:
+            version_info = tuple(int(p) for p in self.host_version.split("."))
+        except ValueError:
+            version_info = ()
+
+        if version_info < (3, 15):
+            # Free-threaded builds had no stable ABI before 3.15.
+            return [] if free_threaded else [".abi3.so"]
+
+        stem = "abi3t" if free_threaded else "abi3"
+        # Plain form first, deliberately: setuptools get_abi3_suffix() returns
+        # the first entry containing ".abi3", and the portable name is the one
+        # we want emitted for a cross build.
+        suffixes = [".%s.so" % stem]
+        soabi_platform = self._host_soabi_platform()
+        if soabi_platform:
+            suffixes.append(".%s-%s.so" % (stem, soabi_platform))
+        return suffixes
+
     def expand_platform_tags(self):
         """
         Convert legacy manylinux tags to PEP600, because pip only looks for one
diff --git a/crossenv/scripts/importlib-machinery-patch.py.tmpl b/crossenv/scripts/importlib-machinery-patch.py.tmpl
index a0bca50..82df061 100644
--- a/crossenv/scripts/importlib-machinery-patch.py.tmpl
+++ b/crossenv/scripts/importlib-machinery-patch.py.tmpl
@@ -29,4 +29,4 @@ def _PathFinder_find_spec(cls, fullname, path=None, target=None):
 
 PathFinder.find_spec = _PathFinder_find_spec
 
-EXTENSION_SUFFIXES = [{{repr(self.sysconfig_ext_suffix)}}, ".abi3.so", ".so"]
+EXTENSION_SUFFIXES = {{repr(self.sysconfig_extension_suffixes)}}
diff --git a/tests/test_environment.py b/tests/test_environment.py
index f0c875e..2721ccb 100644
--- a/tests/test_environment.py
+++ b/tests/test_environment.py
@@ -294,3 +294,52 @@ def test_machine_override(tmp_path, host_python, build_python):
     )
     out = out.strip()
     assert out == "foobar foobar"
+
+
+def test_abi3_extension_suffixes(crossenv):
+    out = crossenv.check_output(
+        [
+            "python",
+            "-c",
+            dedent("""\
+            import sys
+            import sysconfig
+            from importlib.machinery import EXTENSION_SUFFIXES
+            print(sys.version_info.major, sys.version_info.minor)
+            print(1 if sysconfig.get_config_var("Py_GIL_DISABLED") else 0)
+            print(" ".join(EXTENSION_SUFFIXES))
+            """),
+        ],
+        universal_newlines=True,
+    )
+    version_line, gil_line, suffix_line = out.strip().splitlines()
+    version_info = tuple(int(part) for part in version_line.split())
+    free_threaded = gil_line == "1"
+    suffixes = suffix_line.split()
+
+    ext_suffix = suffixes[0]
+    assert suffixes[-1] == ".so"
+
+    abi3 = [suffix for suffix in suffixes if ".abi3" in suffix]
+
+    if version_info < (3, 15):
+        # Free-threaded builds had no stable ABI before 3.15, and the
+        # platform-tagged forms did not exist yet.
+        assert abi3 == ([] if free_threaded else [".abi3.so"])
+        return
+
+    # setuptools get_abi3_suffix() returns the first entry containing ".abi3",
+    # so the untagged form has to come first.
+    stem = ".abi3t" if free_threaded else ".abi3"
+    assert abi3[0] == stem + ".so"
+
+    # A host with a PLATFORM_TRIPLET offers the tagged form too, so the loop
+    # below is not vacuous.
+    if len(ext_suffix[1:-3].split("-")) > 2:
+        assert len(abi3) == 2
+
+    # Any platform-tagged form must carry the host's own tag, not the build
+    # machine's.
+    for suffix in abi3[1:]:
+        tag = suffix.split("-", 1)[1]
+        assert ext_suffix.endswith("-" + tag)