diff --git a/packages/babel-helper-module-transforms/src/rewrite-live-references.ts b/packages/babel-helper-module-transforms/src/rewrite-live-references.ts
index 84a0a8da90d9..8cd814cc7c24 100644
--- a/packages/babel-helper-module-transforms/src/rewrite-live-references.ts
+++ b/packages/babel-helper-module-transforms/src/rewrite-live-references.ts
@@ -350,31 +350,33 @@ const rewriteReferencesVisitor: Visitor<RewriteReferencesVisitorState> = {
   ) {
     const { scope, node } = path;
     const { left } = node;
-    const { exported, scope: programScope } = this;
+    const { exported, imported, scope: programScope } = this;
 
     if (!t.isVariableDeclaration(left)) {
-      let didTransform = false;
-      const bodyPath = path.get("body");
-      const loopBodyScope = bodyPath.scope;
+      let didTransformExport = false,
+        importConstViolationName;
+      const loopBodyScope = path.get("body").scope;
       for (const name of Object.keys(t.getOuterBindingIdentifiers(left))) {
-        if (
-          exported.get(name) &&
-          programScope.getBinding(name) === scope.getBinding(name)
-        ) {
-          didTransform = true;
-          if (loopBodyScope.hasOwnBinding(name)) {
-            loopBodyScope.rename(name);
+        if (programScope.getBinding(name) === scope.getBinding(name)) {
+          if (exported.has(name)) {
+            didTransformExport = true;
+            if (loopBodyScope.hasOwnBinding(name)) {
+              loopBodyScope.rename(name);
+            }
+          }
+          if (imported.has(name) && !importConstViolationName) {
+            importConstViolationName = name;
           }
         }
       }
-      if (!didTransform) {
+      if (!didTransformExport && !importConstViolationName) {
         return;
       }
+
+      path.ensureBlock();
+      const bodyPath = path.get("body");
+
       const newLoopId = scope.generateUidIdentifierBasedOnNode(left);
-      bodyPath.unshiftContainer(
-        "body",
-        t.expressionStatement(t.assignmentExpression("=", left, newLoopId)),
-      );
       path
         .get("left")
         .replaceWith(
@@ -383,6 +385,19 @@ const rewriteReferencesVisitor: Visitor<RewriteReferencesVisitorState> = {
           ]),
         );
       scope.registerDeclaration(path.get("left"));
+
+      if (didTransformExport) {
+        bodyPath.unshiftContainer(
+          "body",
+          t.expressionStatement(t.assignmentExpression("=", left, newLoopId)),
+        );
+      }
+      if (importConstViolationName) {
+        bodyPath.unshiftContainer(
+          "body",
+          t.expressionStatement(buildImportThrow(importConstViolationName)),
+        );
+      }
     }
   },
 };
diff --git a/packages/babel-helper-simple-access/src/index.ts b/packages/babel-helper-simple-access/src/index.ts
index c812f195bacc..27304a32ee0d 100644
--- a/packages/babel-helper-simple-access/src/index.ts
+++ b/packages/babel-helper-simple-access/src/index.ts
@@ -100,12 +100,30 @@ const simpleAssignmentVisitor = {
         return;
       }
 
-      path.node.right = t.binaryExpression(
-        path.node.operator.slice(0, -1),
-        t.cloneNode(path.node.left),
-        path.node.right,
-      );
-      path.node.operator = "=";
+      const operator = path.node.operator.slice(0, -1);
+      if (t.LOGICAL_OPERATORS.includes(operator)) {
+        // &&, ||, ??
+        // (foo &&= bar) => (foo && foo = bar)
+        path.replaceWith(
+          t.logicalExpression(
+            operator,
+            path.node.left,
+            t.assignmentExpression(
+              "=",
+              t.cloneNode(path.node.left),
+              path.node.right,
+            ),
+          ),
+        );
+      } else {
+        // (foo += bar) => (foo = foo + bar)
+        path.node.right = t.binaryExpression(
+          operator,
+          t.cloneNode(path.node.left),
+          path.node.right,
+        );
+        path.node.operator = "=";
+      }
     },
   },
 };
diff --git a/packages/babel-plugin-transform-modules-commonjs/test/fixtures/misc/for-of-in-export/input.mjs b/packages/babel-plugin-transform-modules-commonjs/test/fixtures/misc/for-of-in-export/input.mjs
index fe09208eea2c..8b11f890a175 100644
--- a/packages/babel-plugin-transform-modules-commonjs/test/fixtures/misc/for-of-in-export/input.mjs
+++ b/packages/babel-plugin-transform-modules-commonjs/test/fixtures/misc/for-of-in-export/input.mjs
@@ -16,7 +16,9 @@ for ([foo, [...foo]] of []) {
     let foo;
 }
 
+for (foo of []) ;
+
 {
     let foo;
     for(foo of []) {}
-}
\ No newline at end of file
+}
diff --git a/packages/babel-plugin-transform-modules-commonjs/test/fixtures/misc/for-of-in-export/output.js b/packages/babel-plugin-transform-modules-commonjs/test/fixtures/misc/for-of-in-export/output.js
index bb8330350160..6375528d7646 100644
--- a/packages/babel-plugin-transform-modules-commonjs/test/fixtures/misc/for-of-in-export/output.js
+++ b/packages/babel-plugin-transform-modules-commonjs/test/fixtures/misc/for-of-in-export/output.js
@@ -58,6 +58,11 @@ for (let _ref2 of []) {
   let _foo8;
 }
 
+for (let _foo9 of []) {
+  exports.bar = exports.foo = foo = _foo9;
+  ;
+}
+
 {
   let foo;
 
diff --git a/packages/babel-plugin-transform-modules-commonjs/test/fixtures/misc/import-const-throw/input.mjs b/packages/babel-plugin-transform-modules-commonjs/test/fixtures/misc/import-const-throw/input.mjs
index 899f1394bbb1..650e21b272d8 100644
--- a/packages/babel-plugin-transform-modules-commonjs/test/fixtures/misc/import-const-throw/input.mjs
+++ b/packages/babel-plugin-transform-modules-commonjs/test/fixtures/misc/import-const-throw/input.mjs
@@ -15,3 +15,33 @@ Baz = 44;
 ({prop: Foo} = {});
 ({prop: Bar} = {});
 ({prop: Baz} = {});
+
+Foo += 2;
+Bar += 2;
+Baz += 2;
+
+Foo >>>= 3;
+Bar >>>= 3;
+Baz >>>= 3;
+
+Foo &&= 4;
+Bar &&= 4;
+Baz &&= 4;
+
+--Foo;
+--Bar;
+--Baz;
+
+Foo++;
+Bar++;
+Baz++;
+
+for (Foo in {}) ;
+for (Bar in {}) {}
+for (Baz of []) {
+	let Baz;
+}
+
+for ({Foo} in {}) {}
+for ([Bar] in {}) {}
+for ([...Baz] in {}) {}
diff --git a/packages/babel-plugin-transform-modules-commonjs/test/fixtures/misc/import-const-throw/output.js b/packages/babel-plugin-transform-modules-commonjs/test/fixtures/misc/import-const-throw/output.js
index 01984ae47f96..79d37c0932bf 100644
--- a/packages/babel-plugin-transform-modules-commonjs/test/fixtures/misc/import-const-throw/output.js
+++ b/packages/babel-plugin-transform-modules-commonjs/test/fixtures/misc/import-const-throw/output.js
@@ -47,3 +47,88 @@ _baz.Baz = (44, function () {
 } = ({}, function () {
   throw new Error('"' + "Baz" + '" is read-only.');
 }()));
+_foo.default = (_foo.default + 2, function () {
+  throw new Error('"' + "Foo" + '" is read-only.');
+}());
+Bar = (Bar + 2, function () {
+  throw new Error('"' + "Bar" + '" is read-only.');
+}());
+_baz.Baz = (_baz.Baz + 2, function () {
+  throw new Error('"' + "Baz" + '" is read-only.');
+}());
+_foo.default = (_foo.default >>> 3, function () {
+  throw new Error('"' + "Foo" + '" is read-only.');
+}());
+Bar = (Bar >>> 3, function () {
+  throw new Error('"' + "Bar" + '" is read-only.');
+}());
+_baz.Baz = (_baz.Baz >>> 3, function () {
+  throw new Error('"' + "Baz" + '" is read-only.');
+}());
+_foo.default && (_foo.default = (4, function () {
+  throw new Error('"' + "Foo" + '" is read-only.');
+}()));
+Bar && (Bar = (4, function () {
+  throw new Error('"' + "Bar" + '" is read-only.');
+}()));
+_baz.Baz && (_baz.Baz = (4, function () {
+  throw new Error('"' + "Baz" + '" is read-only.');
+}()));
+_foo.default = (_foo.default - 1, function () {
+  throw new Error('"' + "Foo" + '" is read-only.');
+}());
+Bar = (Bar - 1, function () {
+  throw new Error('"' + "Bar" + '" is read-only.');
+}());
+_baz.Baz = (_baz.Baz - 1, function () {
+  throw new Error('"' + "Baz" + '" is read-only.');
+}());
+_foo.default = (_foo.default + 1, function () {
+  throw new Error('"' + "Foo" + '" is read-only.');
+}());
+Bar = (Bar + 1, function () {
+  throw new Error('"' + "Bar" + '" is read-only.');
+}());
+_baz.Baz = (_baz.Baz + 1, function () {
+  throw new Error('"' + "Baz" + '" is read-only.');
+}());
+
+for (let _Foo in {}) {
+  (function () {
+    throw new Error('"' + "Foo" + '" is read-only.');
+  })();
+
+  ;
+}
+
+for (let _Bar in {}) {
+  (function () {
+    throw new Error('"' + "Bar" + '" is read-only.');
+  })();
+}
+
+for (let _Baz of []) {
+  (function () {
+    throw new Error('"' + "Baz" + '" is read-only.');
+  })();
+
+  let Baz;
+}
+
+for (let _Foo2 in {}) {
+  (function () {
+    throw new Error('"' + "Foo" + '" is read-only.');
+  })();
+}
+
+for (let _ref in {}) {
+  (function () {
+    throw new Error('"' + "Bar" + '" is read-only.');
+  })();
+}
+
+for (let _ref2 in {}) {
+  (function () {
+    throw new Error('"' + "Baz" + '" is read-only.');
+  })();
+}