diff --git a/src/Type/ObjectShapeType.php b/src/Type/ObjectShapeType.php
index 4c45b05744..812b2b706b 100644
--- a/src/Type/ObjectShapeType.php
+++ b/src/Type/ObjectShapeType.php
@@ -178,11 +178,12 @@ public function acceptsWithReason(Type $type, bool $strictTypes): AcceptsResult
 				$otherProperty = $type->getProperty($propertyName, $scope);
 			} catch (MissingPropertyFromReflectionException) {
 				return new AcceptsResult(
-					TrinaryLogic::createNo(),
+					$result->result,
 					[
 						sprintf(
-							'%s does not have property $%s.',
+							'%s %s not have property $%s.',
 							$type->describe(VerbosityLevel::typeOnly()),
+							$result->no() ? 'does' : 'might',
 							$propertyName,
 						),
 					],
@@ -278,7 +279,7 @@ public function isSuperTypeOf(Type $type): TrinaryLogic
 			try {
 				$otherProperty = $type->getProperty($propertyName, $scope);
 			} catch (MissingPropertyFromReflectionException) {
-				return TrinaryLogic::createNo();
+				return $result;
 			}
 
 			if (!$otherProperty->isPublic()) {
diff --git a/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php b/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php
index 95581d836a..b81d2bd964 100644
--- a/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php
+++ b/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php
@@ -2919,7 +2919,7 @@ public function testObjectShapes(): void
 			[
 				'Parameter #1 $o of method ObjectShapesAcceptance\Foo::doBar() expects object{foo: int, bar: string}, Exception given.',
 				14,
-				'Exception does not have property $foo.',
+				'Exception might not have property $foo.',
 			],
 			[
 				'Parameter #1 $o of method ObjectShapesAcceptance\Foo::doBar() expects object{foo: int, bar: string}, object{foo: string, bar: int} given.',
@@ -2989,6 +2989,16 @@ public function testObjectShapes(): void
 				157,
 				'Property ($foo) type int does not accept type string.',
 			],
+			[
+				'Parameter #1 $o of method ObjectShapesAcceptance\TestAcceptance::doFoo() expects object{foo: int}, Traversable given.',
+				209,
+				'Traversable might not have property $foo.',
+			],
+			[
+				'Parameter #1 $o of method ObjectShapesAcceptance\TestAcceptance::doFoo() expects object{foo: int}, ObjectShapesAcceptance\FinalClass given.',
+				210,
+				PHP_VERSION_ID < 80200 ? 'ObjectShapesAcceptance\FinalClass might not have property $foo.' : 'ObjectShapesAcceptance\FinalClass does not have property $foo.',
+			],
 		]);
 	}
 
diff --git a/tests/PHPStan/Rules/Methods/data/object-shapes.php b/tests/PHPStan/Rules/Methods/data/object-shapes.php
index 551bd06f80..248eeecc30 100644
--- a/tests/PHPStan/Rules/Methods/data/object-shapes.php
+++ b/tests/PHPStan/Rules/Methods/data/object-shapes.php
@@ -174,3 +174,41 @@ public function doBaz(object $o): void
 	}
 
 }
+
+final class FinalClass
+{
+
+}
+
+class ClassWithFooIntProperty
+{
+
+	/** @var int */
+	public $foo;
+
+}
+
+class TestAcceptance
+{
+
+	/**
+	 * @param object{foo: int} $o
+	 * @return void
+	 */
+	public function doFoo(object $o): void
+	{
+
+	}
+
+	public function doBar(
+		\Traversable $traversable,
+		FinalClass $finalClass,
+		ClassWithFooIntProperty $classWithFooIntProperty
+	)
+	{
+		$this->doFoo($traversable);
+		$this->doFoo($finalClass);
+		$this->doFoo($classWithFooIntProperty);
+	}
+
+}
diff --git a/tests/PHPStan/Type/TypeCombinatorTest.php b/tests/PHPStan/Type/TypeCombinatorTest.php
index 58a248ec44..206c2aeb7c 100644
--- a/tests/PHPStan/Type/TypeCombinatorTest.php
+++ b/tests/PHPStan/Type/TypeCombinatorTest.php
@@ -13,6 +13,7 @@
 use Exception;
 use InvalidArgumentException;
 use Iterator;
+use ObjectShapesAcceptance\ClassWithFooIntProperty;
 use PHPStan\Fixture\FinalClass;
 use PHPStan\Testing\PHPStanTestCase;
 use PHPStan\Type\Accessory\AccessoryLiteralStringType;
@@ -2396,6 +2397,39 @@ public function dataUnion(): iterable
 			UnionType::class,
 			'object{bar: string}|object{foo: int}',
 		];
+
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+				new ObjectType(Traversable::class),
+			],
+			UnionType::class,
+			'object{foo: int}|Traversable',
+		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+				new ObjectType(\ObjectShape\Foo::class),
+			],
+			UnionType::class,
+			'ObjectShape\Foo|object{foo: int}',
+		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+				new ObjectType(ClassWithFooIntProperty::class),
+			],
+			ObjectShapeType::class,
+			'object{foo: int}',
+		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+				new ObjectType(\ObjectShapesAcceptance\FinalClass::class),
+			],
+			UnionType::class,
+			'ObjectShapesAcceptance\FinalClass|object{foo: int}',
+		];
 	}
 
 	/**
@@ -3936,6 +3970,38 @@ public function dataIntersect(): iterable
 			NeverType::class,
 			'*NEVER*=implicit',
 		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+				new ObjectType(Traversable::class),
+			],
+			IntersectionType::class,
+			'object{foo: int}&Traversable',
+		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+				new ObjectType(\ObjectShapesAcceptance\Foo::class),
+			],
+			IntersectionType::class,
+			'ObjectShapesAcceptance\Foo&object{foo: int}',
+		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+				new ObjectType(ClassWithFooIntProperty::class),
+			],
+			ObjectType::class,
+			'ObjectShapesAcceptance\ClassWithFooIntProperty',
+		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+				new ObjectType(\ObjectShapesAcceptance\FinalClass::class),
+			],
+			PHP_VERSION_ID < 80200 ? IntersectionType::class : NeverType::class,
+			PHP_VERSION_ID < 80200 ? 'ObjectShapesAcceptance\FinalClass&object{foo: int}' : '*NEVER*=implicit',
+		];
 	}
 
 	/**