diff --git a/src/auditwheel/main_repair.py b/src/auditwheel/main_repair.py
index a89de776..3b788bad 100644
--- a/src/auditwheel/main_repair.py
+++ b/src/auditwheel/main_repair.py
@@ -78,6 +78,13 @@ def configure_parser(sub_parsers):
         ),
         default=True,
     )
+    p.add_argument(
+        "--no-set-soname",
+        dest="SET_SONAME",
+        action="store_false",
+        help="Move and rename libraries but don't set their SONAME",
+        default=True,
+    )
     p.add_argument(
         "--strip",
         dest="STRIP",
@@ -176,6 +183,7 @@ def execute(args, p):
             lib_sdir=args.LIB_SDIR,
             out_dir=args.WHEEL_DIR,
             update_tags=args.UPDATE_TAGS,
+            set_soname=args.SET_SONAME,
             patcher=patcher,
             exclude=args.EXCLUDE,
             strip=args.STRIP,
diff --git a/src/auditwheel/repair.py b/src/auditwheel/repair.py
index c172b471..771dd61a 100644
--- a/src/auditwheel/repair.py
+++ b/src/auditwheel/repair.py
@@ -38,6 +38,7 @@ def repair_wheel(
     lib_sdir: str,
     out_dir: str,
     update_tags: bool,
+    set_soname: bool,
     patcher: ElfPatcher,
     exclude: list[str],
     strip: bool = False,
@@ -85,7 +86,7 @@ def repair_wheel(
                         % soname
                     )
 
-                new_soname, new_path = copylib(src_path, dest_dir, patcher)
+                new_soname, new_path = copylib(src_path, dest_dir, patcher, set_soname)
                 soname_map[soname] = (new_soname, new_path)
                 replacements.append((soname, new_soname))
             if replacements:
@@ -126,7 +127,9 @@ def strip_symbols(libraries: Iterable[str]) -> None:
         check_call(["strip", "-s", lib])
 
 
-def copylib(src_path: str, dest_dir: str, patcher: ElfPatcher) -> tuple[str, str]:
+def copylib(
+    src_path: str, dest_dir: str, patcher: ElfPatcher, set_soname: bool
+) -> tuple[str, str]:
     """Graft a shared library from the system into the wheel and update the
     relevant links.
 
@@ -160,7 +163,8 @@ def copylib(src_path: str, dest_dir: str, patcher: ElfPatcher) -> tuple[str, str
     if not statinfo.st_mode & stat.S_IWRITE:
         os.chmod(dest_path, statinfo.st_mode | stat.S_IWRITE)
 
-    patcher.set_soname(dest_path, new_soname)
+    if set_soname:
+        patcher.set_soname(dest_path, new_soname)
 
     if any(itertools.chain(rpaths["rpaths"], rpaths["runpaths"])):
         patcher.set_rpath(dest_path, dest_dir)
diff --git a/tests/integration/test_bundled_wheels.py b/tests/integration/test_bundled_wheels.py
index bf2454b5..2eb9df59 100644
--- a/tests/integration/test_bundled_wheels.py
+++ b/tests/integration/test_bundled_wheels.py
@@ -71,6 +71,7 @@ def test_wheel_source_date_epoch(tmp_path, monkeypatch):
         PLAT="manylinux_2_5_x86_64",
         STRIP=False,
         UPDATE_TAGS=True,
+        SET_SONAME=True,
         WHEEL_DIR=str(wheel_output_path),
         WHEEL_FILE=[str(wheel_path)],
         EXCLUDE=[],