diff --git a/libstdc++-v3/include/bits/version.def b/libstdc++-v3/include/bits/version.def
index 412b9ce96f8a..bbc8d383938f 100644
--- a/libstdc++-v3/include/bits/version.def
+++ b/libstdc++-v3/include/bits/version.def
@@ -879,8 +879,12 @@ ftms = {
 
 ftms = {
   name = concepts;
+  // 201806 P0898R3 Standard Library Concepts
+  // 201907 P1754R1 Rename concepts to standard_case for C++20
+  // 202002 P1964R2 Wording for boolean-testable
+  // 202207 P2404R3 Move-only types for equality_comparable_with, etc.
   values = {
-    v = 202002;
+    v = 202207;
     cxxmin = 20;
     extra_cond = "__cpp_concepts >= 201907L";
   };
diff --git a/libstdc++-v3/include/bits/version.h b/libstdc++-v3/include/bits/version.h
index 2b96934ca099..7ee9ae84215e 100644
--- a/libstdc++-v3/include/bits/version.h
+++ b/libstdc++-v3/include/bits/version.h
@@ -985,9 +985,9 @@
 
 #if !defined(__cpp_lib_concepts)
 # if (__cplusplus >= 202002L) && (__cpp_concepts >= 201907L)
-#  define __glibcxx_concepts 202002L
+#  define __glibcxx_concepts 202207L
 #  if defined(__glibcxx_want_all) || defined(__glibcxx_want_concepts)
-#   define __cpp_lib_concepts 202002L
+#   define __cpp_lib_concepts 202207L
 #  endif
 # endif
 #endif /* !defined(__cpp_lib_concepts) */
diff --git a/libstdc++-v3/include/std/concepts b/libstdc++-v3/include/std/concepts
index d9920a8f20a8..870b0a47eab1 100644
--- a/libstdc++-v3/include/std/concepts
+++ b/libstdc++-v3/include/std/concepts
@@ -296,6 +296,27 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
 	  { { !static_cast<_Tp&&>(__t) } -> __boolean_testable_impl; };
   } // namespace __detail
 
+  // [concept.comparisoncommontype], helpers for comparison common types
+  namespace __detail
+  {
+    template<typename _Tp, typename _Up,
+	     typename _Cref = common_reference_t<const _Tp&, const _Up&>>
+      concept __comparison_common_type_with_impl
+	= same_as<common_reference_t<const _Tp&, const _Up&>,
+		  common_reference_t<const _Up&, const _Tp&>>
+	    && requires {
+	      requires convertible_to<const _Tp&, const _Cref&>
+		|| convertible_to<_Tp, const _Cref&>;
+	      requires convertible_to<const _Up&, const _Cref&>
+		|| convertible_to<_Up, const _Cref&>;
+	    };
+
+    template<typename _Tp, typename _Up>
+      concept __comparison_common_type_with
+	= __comparison_common_type_with_impl<remove_cvref_t<_Tp>,
+					     remove_cvref_t<_Up>>;
+  } // namespace __detail
+
   // [concept.equalitycomparable], concept equality_comparable
 
   namespace __detail
@@ -316,7 +337,7 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
   template<typename _Tp, typename _Up>
     concept equality_comparable_with
       = equality_comparable<_Tp> && equality_comparable<_Up>
-      && common_reference_with<__detail::__cref<_Tp>, __detail::__cref<_Up>>
+      && __detail::__comparison_common_type_with<_Tp, _Up>
       && equality_comparable<common_reference_t<__detail::__cref<_Tp>,
 						__detail::__cref<_Up>>>
       && __detail::__weakly_eq_cmp_with<_Tp, _Up>;
diff --git a/libstdc++-v3/libsupc++/compare b/libstdc++-v3/libsupc++/compare
index 08f2b2ba47ed..5b4f47a94e3b 100644
--- a/libstdc++-v3/libsupc++/compare
+++ b/libstdc++-v3/libsupc++/compare
@@ -34,6 +34,7 @@
 #pragma GCC system_header
 #endif
 
+#define __glibcxx_want_concepts
 #define __glibcxx_want_three_way_comparison
 #define __glibcxx_want_type_order
 #include <bits/version.h>
@@ -499,10 +500,8 @@ namespace std _GLIBCXX_VISIBILITY(default)
 
   template<typename _Tp, typename _Up, typename _Cat = partial_ordering>
     concept three_way_comparable_with
-      = three_way_comparable<_Tp, _Cat>
-      && three_way_comparable<_Up, _Cat>
-      && common_reference_with<const remove_reference_t<_Tp>&,
-			       const remove_reference_t<_Up>&>
+      = three_way_comparable<_Tp, _Cat> && three_way_comparable<_Up, _Cat>
+      && __detail::__comparison_common_type_with<_Tp, _Up>
       && three_way_comparable<
 	  common_reference_t<const remove_reference_t<_Tp>&,
 			     const remove_reference_t<_Up>&>, _Cat>
diff --git a/libstdc++-v3/testsuite/std/concepts/concepts.compare/move_only.cc b/libstdc++-v3/testsuite/std/concepts/concepts.compare/move_only.cc
new file mode 100644
index 000000000000..01870d846267
--- /dev/null
+++ b/libstdc++-v3/testsuite/std/concepts/concepts.compare/move_only.cc
@@ -0,0 +1,28 @@
+// { dg-do compile { target c++20 } }
+
+#include <concepts>
+#include <compare>
+
+// P2404R3 Move-only types for equality_comparable_with,
+// totally_ordered_with, and three_way_comparable_with
+
+// This was approved for C++23 but we treat it as a DR for C++20.
+
+#ifndef __cpp_lib_concepts
+# error "Feature-test macro __cpp_lib_concepts is missing in <compare>"
+#elif __cpp_lib_concepts < 202207L
+# error "Feature-test macro __cpp_lib_concepts has wrong value in <compare>"
+#endif
+
+struct MoveOnly
+{
+  MoveOnly(int);
+  MoveOnly(MoveOnly&&) = default;
+  auto operator<=>(const MoveOnly&) const = default;
+  std::strong_ordering operator<=>(int) const;
+  bool operator==(const MoveOnly&) const;
+};
+
+static_assert(std::equality_comparable_with<MoveOnly, int>);
+static_assert(std::totally_ordered_with<MoveOnly, int>);
+static_assert(std::three_way_comparable_with<MoveOnly, int>);