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 | --- a/setuptools/command/install_lib.py
+++ b/setuptools/command/install_lib.py
@@ -15,6 +15,18 @@ class install_lib(orig.install_lib):
 
     distribution: Distribution  # override distutils.dist.Distribution with setuptools.dist.Distribution
 
+    def initialize_options(self):
+        orig.install_lib.initialize_options(self)
+        self.multiarch = None
+        self.install_layout = None
+
+    def finalize_options(self):
+        orig.install_lib.finalize_options(self)
+        self.set_undefined_options('install',('install_layout','install_layout'))
+        if self.install_layout == 'deb' and sys.version_info[:2] >= (3, 3):
+            import sysconfig
+            self.multiarch = sysconfig.get_config_var('MULTIARCH')
+
     def run(self) -> None:
         self.build()
         outfiles = self.install()
@@ -107,6 +119,8 @@ class install_lib(orig.install_lib):
         exclude = self.get_exclusions()
 
         if not exclude:
+            import distutils.dir_util
+            distutils.dir_util._multiarch = self.multiarch
             return orig.install_lib.copy_tree(self, infile, outfile)
 
         # Exclude namespace package __init__.py* files from the output
@@ -117,11 +131,23 @@ class install_lib(orig.install_lib):
 
         outfiles: list[str] = []
 
+        if self.multiarch:
+            import sysconfig
+            ext_suffix = sysconfig.get_config_var ('EXT_SUFFIX')
+            if ext_suffix.endswith(self.multiarch + ext_suffix[-3:]):
+                new_suffix = None
+            else:
+                new_suffix = "%s-%s%s" % (ext_suffix[:-3], self.multiarch, ext_suffix[-3:])
+
         def pf(src: str, dst: str):
             if dst in exclude:
                 log.warn("Skipping installation of %s (namespace package)", dst)
                 return False
 
+            if self.multiarch and new_suffix and dst.endswith(ext_suffix) and not dst.endswith(new_suffix):
+                dst = dst.replace(ext_suffix, new_suffix)
+                log.info("renaming extension to %s", os.path.basename(dst))
+
             log.info("copying %s -> %s", src, os.path.dirname(dst))
             outfiles.append(dst)
             return dst
 |