diff --git a/changelog/10617.feature.rst b/changelog/10617.feature.rst
new file mode 100644
index 000000000..c99ec4889
--- /dev/null
+++ b/changelog/10617.feature.rst
@@ -0,0 +1,2 @@
+Added more comprehensive set assertion rewrites for comparisons other than equality ``==``, with
+the following operations now providing better failure messages: ``!=``, ``<=``, ``>=``, ``<``, and ``>``.
diff --git a/src/_pytest/assertion/util.py b/src/_pytest/assertion/util.py
index 01534797d..057352cd3 100644
--- a/src/_pytest/assertion/util.py
+++ b/src/_pytest/assertion/util.py
@@ -193,6 +193,22 @@ def assertrepr_compare(
         elif op == "not in":
             if istext(left) and istext(right):
                 explanation = _notin_text(left, right, verbose)
+        elif op == "!=":
+            if isset(left) and isset(right):
+                explanation = ["Both sets are equal"]
+        elif op == ">=":
+            if isset(left) and isset(right):
+                explanation = _compare_gte_set(left, right, verbose)
+        elif op == "<=":
+            if isset(left) and isset(right):
+                explanation = _compare_lte_set(left, right, verbose)
+        elif op == ">":
+            if isset(left) and isset(right):
+                explanation = _compare_gt_set(left, right, verbose)
+        elif op == "<":
+            if isset(left) and isset(right):
+                explanation = _compare_lt_set(left, right, verbose)
+
     except outcomes.Exit:
         raise
     except Exception:
@@ -392,15 +408,49 @@ def _compare_eq_set(
     left: AbstractSet[Any], right: AbstractSet[Any], verbose: int = 0
 ) -> List[str]:
     explanation = []
-    diff_left = left - right
-    diff_right = right - left
-    if diff_left:
-        explanation.append("Extra items in the left set:")
-        for item in diff_left:
-            explanation.append(saferepr(item))
-    if diff_right:
-        explanation.append("Extra items in the right set:")
-        for item in diff_right:
+    explanation.extend(_set_one_sided_diff("left", left, right))
+    explanation.extend(_set_one_sided_diff("right", right, left))
+    return explanation
+
+
+def _compare_gt_set(
+    left: AbstractSet[Any], right: AbstractSet[Any], verbose: int = 0
+) -> List[str]:
+    explanation = _compare_gte_set(left, right, verbose)
+    if not explanation:
+        return ["Both sets are equal"]
+    return explanation
+
+
+def _compare_lt_set(
+    left: AbstractSet[Any], right: AbstractSet[Any], verbose: int = 0
+) -> List[str]:
+    explanation = _compare_lte_set(left, right, verbose)
+    if not explanation:
+        return ["Both sets are equal"]
+    return explanation
+
+
+def _compare_gte_set(
+    left: AbstractSet[Any], right: AbstractSet[Any], verbose: int = 0
+) -> List[str]:
+    return _set_one_sided_diff("right", right, left)
+
+
+def _compare_lte_set(
+    left: AbstractSet[Any], right: AbstractSet[Any], verbose: int = 0
+) -> List[str]:
+    return _set_one_sided_diff("left", left, right)
+
+
+def _set_one_sided_diff(
+    posn: str, set1: AbstractSet[Any], set2: AbstractSet[Any]
+) -> List[str]:
+    explanation = []
+    diff = set1 - set2
+    if diff:
+        explanation.append(f"Extra items in the {posn} set:")
+        for item in diff:
             explanation.append(saferepr(item))
     return explanation
 
diff --git a/testing/test_assertion.py b/testing/test_assertion.py
index c04c31f31..d3caa5e48 100644
--- a/testing/test_assertion.py
+++ b/testing/test_assertion.py
@@ -1345,48 +1345,80 @@ def test_reprcompare_whitespaces() -> None:
     ]
 
 
-def test_pytest_assertrepr_compare_integration(pytester: Pytester) -> None:
-    pytester.makepyfile(
+class TestSetAssertions:
+    @pytest.mark.parametrize("op", [">=", ">", "<=", "<", "=="])
+    def test_set_extra_item(self, op, pytester: Pytester) -> None:
+        pytester.makepyfile(
+            f"""
+            def test_hello():
+                x = set("hello x")
+                y = set("hello y")
+                assert x {op} y
         """
-        def test_hello():
-            x = set(range(100))
-            y = x.copy()
-            y.remove(50)
-            assert x == y
-    """
-    )
-    result = pytester.runpytest()
-    result.stdout.fnmatch_lines(
-        [
-            "*def test_hello():*",
-            "*assert x == y*",
-            "*E*Extra items*left*",
-            "*E*50*",
-            "*= 1 failed in*",
-        ]
-    )
+        )
 
+        result = pytester.runpytest()
+        result.stdout.fnmatch_lines(
+            [
+                "*def test_hello():*",
+                f"*assert x {op} y*",
+            ]
+        )
+        if op in [">=", ">", "=="]:
+            result.stdout.fnmatch_lines(
+                [
+                    "*E*Extra items in the right set:*",
+                    "*E*'y'",
+                ]
+            )
+        if op in ["<=", "<", "=="]:
+            result.stdout.fnmatch_lines(
+                [
+                    "*E*Extra items in the left set:*",
+                    "*E*'x'",
+                ]
+            )
 
-def test_sequence_comparison_uses_repr(pytester: Pytester) -> None:
-    pytester.makepyfile(
+    @pytest.mark.parametrize("op", [">", "<", "!="])
+    def test_set_proper_superset_equal(self, pytester: Pytester, op) -> None:
+        pytester.makepyfile(
+            f"""
+            def test_hello():
+                x = set([1, 2, 3])
+                y = x.copy()
+                assert x {op} y
         """
-        def test_hello():
-            x = set("hello x")
-            y = set("hello y")
-            assert x == y
-    """
-    )
-    result = pytester.runpytest()
-    result.stdout.fnmatch_lines(
-        [
-            "*def test_hello():*",
-            "*assert x == y*",
-            "*E*Extra items*left*",
-            "*E*'x'*",
-            "*E*Extra items*right*",
-            "*E*'y'*",
-        ]
-    )
+        )
+
+        result = pytester.runpytest()
+        result.stdout.fnmatch_lines(
+            [
+                "*def test_hello():*",
+                f"*assert x {op} y*",
+                "*E*Both sets are equal*",
+            ]
+        )
+
+    def test_pytest_assertrepr_compare_integration(self, pytester: Pytester) -> None:
+        pytester.makepyfile(
+            """
+            def test_hello():
+                x = set(range(100))
+                y = x.copy()
+                y.remove(50)
+                assert x == y
+        """
+        )
+        result = pytester.runpytest()
+        result.stdout.fnmatch_lines(
+            [
+                "*def test_hello():*",
+                "*assert x == y*",
+                "*E*Extra items*left*",
+                "*E*50*",
+                "*= 1 failed in*",
+            ]
+        )
 
 
 def test_assertrepr_loaded_per_dir(pytester: Pytester) -> None: