diff --git a/src/auditwheel/patcher.py b/src/auditwheel/patcher.py
index 55398665..bc797ec6 100644
--- a/src/auditwheel/patcher.py
+++ b/src/auditwheel/patcher.py
@@ -1,10 +1,12 @@
 import re
 from distutils.spawn import find_executable
+from itertools import chain
 from subprocess import CalledProcessError, check_call, check_output
+from typing import Tuple
 
 
 class ElfPatcher:
-    def replace_needed(self, file_name: str, so_name: str, new_so_name: str) -> None:
+    def replace_needed(self, file_name: str, *old_new_pairs: Tuple[str, str]) -> None:
         raise NotImplementedError
 
     def set_soname(self, file_name: str, new_so_name: str) -> None:
@@ -41,8 +43,16 @@ class Patchelf(ElfPatcher):
     def __init__(self) -> None:
         _verify_patchelf()
 
-    def replace_needed(self, file_name: str, so_name: str, new_so_name: str) -> None:
-        check_call(["patchelf", "--replace-needed", so_name, new_so_name, file_name])
+    def replace_needed(self, file_name: str, *old_new_pairs: Tuple[str, str]) -> None:
+        check_call(
+            [
+                "patchelf",
+                *chain.from_iterable(
+                    ("--replace-needed", *pair) for pair in old_new_pairs
+                ),
+                file_name,
+            ]
+        )
 
     def set_soname(self, file_name: str, new_so_name: str) -> None:
         check_call(["patchelf", "--set-soname", new_so_name, file_name])
diff --git a/src/auditwheel/repair.py b/src/auditwheel/repair.py
index c3386aec..4edb6250 100644
--- a/src/auditwheel/repair.py
+++ b/src/auditwheel/repair.py
@@ -67,8 +67,8 @@ def repair_wheel(
         # here, fn is a path to a python extension library in
         # the wheel, and v['libs'] contains its required libs
         for fn, v in external_refs_by_fn.items():
-
             ext_libs = v[abis[0]]["libs"]  # type: Dict[str, str]
+            replacements = []  # type: List[Tuple[str, str]]
             for soname, src_path in ext_libs.items():
                 if src_path is None:
                     raise ValueError(
@@ -81,7 +81,9 @@ def repair_wheel(
 
                 new_soname, new_path = copylib(src_path, dest_dir, patcher)
                 soname_map[soname] = (new_soname, new_path)
-                patcher.replace_needed(fn, soname, new_soname)
+                replacements.append((soname, new_soname))
+            if replacements:
+                patcher.replace_needed(fn, *replacements)
 
             if len(ext_libs) > 0:
                 new_rpath = os.path.relpath(dest_dir, os.path.dirname(fn))
@@ -94,9 +96,12 @@ def repair_wheel(
         # name of the other.
         for old_soname, (new_soname, path) in soname_map.items():
             needed = elf_read_dt_needed(path)
+            replacements = []
             for n in needed:
                 if n in soname_map:
-                    patcher.replace_needed(path, n, soname_map[n][0])
+                    replacements.append((n, soname_map[n][0]))
+            if replacements:
+                patcher.replace_needed(path, *replacements)
 
         if update_tags:
             ctx.out_wheel = add_platforms(ctx, abis, get_replace_platforms(abis[0]))
diff --git a/tests/unit/test_elfpatcher.py b/tests/unit/test_elfpatcher.py
index ccca54aa..62f10d8b 100644
--- a/tests/unit/test_elfpatcher.py
+++ b/tests/unit/test_elfpatcher.py
@@ -41,16 +41,35 @@ def test_patchelf_version_check_fail(check_output, version):
 class TestPatchElf:
     """ "Validate that patchelf is invoked with the correct arguments."""
 
-    def test_replace_needed(self, check_call, _0, _1):
+    def test_replace_needed_one(self, check_call, _0, _1):
         patcher = Patchelf()
         filename = "test.so"
         soname_old = "TEST_OLD"
         soname_new = "TEST_NEW"
-        patcher.replace_needed(filename, soname_old, soname_new)
+        patcher.replace_needed(filename, (soname_old, soname_new))
         check_call.assert_called_once_with(
             ["patchelf", "--replace-needed", soname_old, soname_new, filename]
         )
 
+    def test_replace_needed_multple(self, check_call, _0, _1):
+        patcher = Patchelf()
+        filename = "test.so"
+        replacements = [
+            ("TEST_OLD1", "TEST_NEW1"),
+            ("TEST_OLD2", "TEST_NEW2"),
+        ]
+        patcher.replace_needed(filename, *replacements)
+        check_call.assert_called_once_with(
+            [
+                "patchelf",
+                "--replace-needed",
+                *replacements[0],
+                "--replace-needed",
+                *replacements[1],
+                filename,
+            ]
+        )
+
     def test_set_soname(self, check_call, _0, _1):
         patcher = Patchelf()
         filename = "test.so"