diff --git a/src/Psalm/Internal/Codebase/Methods.php b/src/Psalm/Internal/Codebase/Methods.php
index 940edc9c472..459f8496e3e 100644
--- a/src/Psalm/Internal/Codebase/Methods.php
+++ b/src/Psalm/Internal/Codebase/Methods.php
@@ -768,8 +768,10 @@ public function getMethodReturnType(
                     $candidate_type
                 );
 
-                if ((!$old_contained_by_new && !$new_contained_by_old)
-                    || ($old_contained_by_new && $new_contained_by_old)
+                if (((!$old_contained_by_new && !$new_contained_by_old)
+                    || ($old_contained_by_new && $new_contained_by_old))
+                    && !$candidate_type->hasTemplate()
+                    && !$overridden_storage->return_type->hasTemplate()
                 ) {
                     $attempted_intersection = null;
                     if ($old_contained_by_new) { //implicitly $new_contained_by_old as well
diff --git a/tests/Template/ClassTemplateTest.php b/tests/Template/ClassTemplateTest.php
index f447f8d8c00..6c40d7a031b 100644
--- a/tests/Template/ClassTemplateTest.php
+++ b/tests/Template/ClassTemplateTest.php
@@ -16,6 +16,49 @@ class ClassTemplateTest extends TestCase
     public function providerValidCodeParse(): iterable
     {
         return [
+            'templateIntersection' => [
+                'code' => '<?php
+                    interface EntityInterface
+                    {
+                        public function getId(): string;
+                    }
+
+                    /**
+                     * @phpstan-template T of EntityInterface
+                     */
+                    interface RepositoryInterface
+                    {
+                        /**
+                         * @return T|null
+                         */
+                    public function byId(string $id);
+                    }
+
+                    final class Foo implements EntityInterface
+                    {
+                        public function getId(): string
+                        {
+                            return "42";
+                        }
+                    }
+
+                    /**
+                     * @phpstan-implements RepositoryInterface<Foo>
+                     */
+                    final class FooRepository implements RepositoryInterface
+                    {
+                        /**
+                         * @var Foo[]
+                         */
+                        public array $elements = [];
+
+                        public function byId(string $id): ?Foo
+                        {
+                            return $this->elements[$id] ?? null;
+                        }
+                    }
+                '
+            ],
             'cachingIterator' => [
                 'code' => '<?php