diff --git a/phpstan-baseline.neon b/phpstan-baseline.neon
index 6906e22da9..b18d053ae7 100644
--- a/phpstan-baseline.neon
+++ b/phpstan-baseline.neon
@@ -1734,7 +1734,7 @@ parameters:
 		-
 			rawMessage: 'Doing instanceof PHPStan\Type\ObjectShapeType is error-prone and deprecated. Use Type::isObject() and Type::hasProperty() instead.'
 			identifier: phpstanApi.instanceofType
-			count: 2
+			count: 4
 			path: src/Type/TypeCombinator.php
 
 		-
diff --git a/src/Type/ObjectShapeType.php b/src/Type/ObjectShapeType.php
index 9dedcfa148..78a89a87b5 100644
--- a/src/Type/ObjectShapeType.php
+++ b/src/Type/ObjectShapeType.php
@@ -10,6 +10,7 @@
 use PHPStan\PhpDocParser\Ast\Type\ObjectShapeNode;
 use PHPStan\PhpDocParser\Ast\Type\TypeNode;
 use PHPStan\Reflection\ClassMemberAccessAnswerer;
+use PHPStan\Reflection\Dummy\DummyPropertyReflection;
 use PHPStan\Reflection\ExtendedPropertyReflection;
 use PHPStan\Reflection\MissingPropertyFromReflectionException;
 use PHPStan\Reflection\Php\UniversalObjectCratesClassReflectionExtension;
@@ -113,15 +114,14 @@ public function getUnresolvedPropertyPrototype(string $propertyName, ClassMember
 
 	public function hasInstanceProperty(string $propertyName): TrinaryLogic
 	{
-		if (!array_key_exists($propertyName, $this->properties)) {
-			return TrinaryLogic::createNo();
+		if (
+			array_key_exists($propertyName, $this->properties)
+			&& !in_array($propertyName, $this->optionalProperties, true)
+		) {
+			return TrinaryLogic::createYes();
 		}
 
-		if (in_array($propertyName, $this->optionalProperties, true)) {
-			return TrinaryLogic::createMaybe();
-		}
-
-		return TrinaryLogic::createYes();
+		return TrinaryLogic::createMaybe();
 	}
 
 	public function getInstanceProperty(string $propertyName, ClassMemberAccessAnswerer $scope): ExtendedPropertyReflection
@@ -131,11 +131,12 @@ public function getInstanceProperty(string $propertyName, ClassMemberAccessAnswe
 
 	public function getUnresolvedInstancePropertyPrototype(string $propertyName, ClassMemberAccessAnswerer $scope): UnresolvedPropertyPrototypeReflection
 	{
-		if (!array_key_exists($propertyName, $this->properties)) {
-			throw new ShouldNotHappenException();
+		if (array_key_exists($propertyName, $this->properties)) {
+			$property = new ObjectShapePropertyReflection($propertyName, $this->properties[$propertyName]);
+		} else {
+			$property = new DummyPropertyReflection($propertyName);
 		}
 
-		$property = new ObjectShapePropertyReflection($propertyName, $this->properties[$propertyName]);
 		return new CallbackUnresolvedPropertyPrototypeReflection(
 			$property,
 			$property->getDeclaringClass(),
diff --git a/src/Type/TypeCombinator.php b/src/Type/TypeCombinator.php
index e7a0d6bdf5..28f3ec5354 100644
--- a/src/Type/TypeCombinator.php
+++ b/src/Type/TypeCombinator.php
@@ -26,6 +26,7 @@
 use PHPStan\Type\Generic\TemplateType;
 use PHPStan\Type\Generic\TemplateTypeFactory;
 use PHPStan\Type\Generic\TemplateUnionType;
+use function array_filter;
 use function array_key_exists;
 use function array_key_first;
 use function array_merge;
@@ -36,6 +37,7 @@
 use function get_class;
 use function in_array;
 use function is_int;
+use function ksort;
 use function sprintf;
 use function usort;
 use const PHP_INT_MAX;
@@ -1300,6 +1302,81 @@ public static function intersect(Type ...$types): Type
 					}
 				}
 
+				if ($types[$i] instanceof ObjectShapeType && $types[$j] instanceof ObjectShapeType) {
+					$mergedProperties = $types[$i]->getProperties();
+					$mergedOptionalProperties = $types[$i]->getOptionalProperties();
+					foreach ($types[$j]->getProperties() as $propertyName => $propertyType) {
+						if (array_key_exists($propertyName, $mergedProperties)) {
+							$intersectedPropertyType = self::intersect($mergedProperties[$propertyName], $propertyType);
+							if ($intersectedPropertyType instanceof NeverType) {
+								if (
+									in_array($propertyName, $mergedOptionalProperties, true)
+									&& in_array($propertyName, $types[$j]->getOptionalProperties(), true)
+								) {
+									unset($mergedProperties[$propertyName]);
+									$mergedOptionalProperties = array_values(array_filter(
+										$mergedOptionalProperties,
+										static fn ($p) => $p !== $propertyName,
+									));
+									continue;
+								}
+
+								return new NeverType();
+							}
+							$mergedProperties[$propertyName] = $intersectedPropertyType;
+							if (
+								in_array($propertyName, $mergedOptionalProperties, true)
+								&& !in_array($propertyName, $types[$j]->getOptionalProperties(), true)
+							) {
+								$mergedOptionalProperties = array_values(array_filter(
+									$mergedOptionalProperties,
+									static fn ($p) => $p !== $propertyName,
+								));
+							}
+						} else {
+							$mergedProperties[$propertyName] = $propertyType;
+							if (in_array($propertyName, $types[$j]->getOptionalProperties(), true)) {
+								$mergedOptionalProperties[] = $propertyName;
+							}
+						}
+					}
+					ksort($mergedProperties);
+					$types[$i] = new ObjectShapeType($mergedProperties, $mergedOptionalProperties);
+					array_splice($types, $j--, 1);
+					$typesCount--;
+					continue;
+				}
+
+				if ($types[$i] instanceof ObjectShapeType && $types[$j] instanceof HasPropertyType) {
+					$propertyName = $types[$j]->getPropertyName();
+					if (!array_key_exists($propertyName, $types[$i]->getProperties())) {
+						$properties = $types[$i]->getProperties();
+						$properties[$propertyName] = new MixedType();
+						ksort($properties);
+						$types[$i] = new ObjectShapeType($properties, $types[$i]->getOptionalProperties());
+					} else {
+						$types[$i] = $types[$i]->makePropertyRequired($propertyName);
+					}
+					array_splice($types, $j--, 1);
+					$typesCount--;
+					continue;
+				}
+
+				if ($types[$j] instanceof ObjectShapeType && $types[$i] instanceof HasPropertyType) {
+					$propertyName = $types[$i]->getPropertyName();
+					if (!array_key_exists($propertyName, $types[$j]->getProperties())) {
+						$properties = $types[$j]->getProperties();
+						$properties[$propertyName] = new MixedType();
+						ksort($properties);
+						$types[$j] = new ObjectShapeType($properties, $types[$j]->getOptionalProperties());
+					} else {
+						$types[$j] = $types[$j]->makePropertyRequired($propertyName);
+					}
+					array_splice($types, $i--, 1);
+					$typesCount--;
+					continue 2;
+				}
+
 				if ($types[$j] instanceof IterableType) {
 					$isSuperTypeA = $types[$j]->isSuperTypeOfMixed($types[$i]);
 				} else {
@@ -1410,20 +1487,6 @@ public static function intersect(Type ...$types): Type
 						continue 2;
 					}
 
-					if ($types[$i] instanceof ObjectShapeType && $types[$j] instanceof HasPropertyType) {
-						$types[$i] = $types[$i]->makePropertyRequired($types[$j]->getPropertyName());
-						array_splice($types, $j--, 1);
-						$typesCount--;
-						continue;
-					}
-
-					if ($types[$j] instanceof ObjectShapeType && $types[$i] instanceof HasPropertyType) {
-						$types[$j] = $types[$j]->makePropertyRequired($types[$i]->getPropertyName());
-						array_splice($types, $i--, 1);
-						$typesCount--;
-						continue 2;
-					}
-
 					if ($types[$i] instanceof ConstantArrayType && ($types[$j] instanceof ArrayType || $types[$j] instanceof ConstantArrayType)) {
 						$newArray = ConstantArrayTypeBuilder::createEmpty();
 						$valueTypes = $types[$i]->getValueTypes();
diff --git a/tests/PHPStan/Analyser/nsrt/bug-13227.php b/tests/PHPStan/Analyser/nsrt/bug-13227.php
new file mode 100644
index 0000000000..209bc84d75
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-13227.php
@@ -0,0 +1,29 @@
+<?php
+
+namespace Bug13227;
+
+use function PHPStan\Testing\assertType;
+
+/**
+ * @phpstan-type Type1 object{ a: int }
+ * @phpstan-type Type2 Type1 & object{ b: int }
+ * @phpstan-type Type3 object{ a: int, b?: string } & object{ b: string, c?: int }
+ */
+class Foo
+{
+	/**
+	 * @param Type2 $x
+	 */
+	public function doFoo($x): void
+	{
+		assertType('object{a: int, b: int}', $x);
+	}
+
+	/**
+	 * @param Type3 $y
+	 */
+	public function doBar($y): void
+	{
+		assertType('object{a: int, b: string, c?: int}', $y);
+	}
+}
diff --git a/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeFunctionCallRuleTest.php b/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeFunctionCallRuleTest.php
index 69e992139d..7407ac04aa 100644
--- a/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeFunctionCallRuleTest.php
+++ b/tests/PHPStan/Rules/Comparison/ImpossibleCheckTypeFunctionCallRuleTest.php
@@ -721,13 +721,7 @@ public function testReportAlwaysTrueInLastCondition(bool $reportAlwaysTrueInLast
 	public function testObjectShapes(): void
 	{
 		$this->treatPhpDocTypesAsCertain = true;
-		$this->analyse([__DIR__ . '/data/property-exists-object-shapes.php'], [
-			[
-				'Call to function property_exists() with object{foo: int, bar?: string} and \'baz\' will always evaluate to false.',
-				24,
-				'Because the type is coming from a PHPDoc, you can turn off this check by setting <fg=cyan>treatPhpDocTypesAsCertain: false</> in your <fg=cyan>%configurationFile%</>.',
-			],
-		]);
+		$this->analyse([__DIR__ . '/data/property-exists-object-shapes.php'], []);
 	}
 
 	/** @return list<array{0: string, 1: int, 2?: string}> */
diff --git a/tests/PHPStan/Type/ObjectShapeTypeTest.php b/tests/PHPStan/Type/ObjectShapeTypeTest.php
new file mode 100644
index 0000000000..f66e2a8234
--- /dev/null
+++ b/tests/PHPStan/Type/ObjectShapeTypeTest.php
@@ -0,0 +1,159 @@
+<?php declare(strict_types = 1);
+
+namespace PHPStan\Type;
+
+use PHPStan\Testing\PHPStanTestCase;
+use PHPStan\TrinaryLogic;
+use PHPStan\Type\Constant\ConstantIntegerType;
+use PHPUnit\Framework\Attributes\DataProvider;
+use function sprintf;
+
+class ObjectShapeTypeTest extends PHPStanTestCase
+{
+
+	public static function dataIsSuperTypeOf(): iterable
+	{
+		// Same properties, same types
+		yield [
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			TrinaryLogic::createYes(),
+		];
+
+		// Wider property type is supertype
+		yield [
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			new ObjectShapeType(['foo' => new ConstantIntegerType(1)], []),
+			TrinaryLogic::createYes(),
+		];
+
+		// Narrower property type is maybe supertype
+		yield [
+			new ObjectShapeType(['foo' => new ConstantIntegerType(1)], []),
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			TrinaryLogic::createMaybe(),
+		];
+
+		// Incompatible property types
+		yield [
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			new ObjectShapeType(['foo' => new StringType()], []),
+			TrinaryLogic::createNo(),
+		];
+
+		// Disjoint properties - object shapes are open types
+		yield [
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			new ObjectShapeType(['bar' => new StringType()], []),
+			TrinaryLogic::createMaybe(),
+		];
+
+		yield [
+			new ObjectShapeType(['bar' => new StringType()], []),
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			TrinaryLogic::createMaybe(),
+		];
+
+		// Required vs optional: optional is supertype of required
+		yield [
+			new ObjectShapeType(['foo' => new IntegerType()], ['foo']),
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			TrinaryLogic::createYes(),
+		];
+
+		// Required vs optional: required is maybe supertype of optional
+		yield [
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			new ObjectShapeType(['foo' => new IntegerType()], ['foo']),
+			TrinaryLogic::createMaybe(),
+		];
+
+		// Wider type with required property
+		yield [
+			new ObjectShapeType(['foo' => TypeCombinator::union(new IntegerType(), new NullType())], []),
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			TrinaryLogic::createYes(),
+		];
+
+		// Narrower type checking wider
+		yield [
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			new ObjectShapeType(['foo' => TypeCombinator::union(new IntegerType(), new NullType())], []),
+			TrinaryLogic::createMaybe(),
+		];
+
+		// Optional wider type vs required narrower
+		yield [
+			new ObjectShapeType(['foo' => TypeCombinator::union(new IntegerType(), new NullType())], ['foo']),
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			TrinaryLogic::createYes(),
+		];
+
+		// Required narrower vs optional wider
+		yield [
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			new ObjectShapeType(['foo' => TypeCombinator::union(new IntegerType(), new NullType())], ['foo']),
+			TrinaryLogic::createMaybe(),
+		];
+
+		// Disjoint with optional property
+		yield [
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			new ObjectShapeType(['bar' => new IntegerType()], ['bar']),
+			TrinaryLogic::createMaybe(),
+		];
+
+		yield [
+			new ObjectShapeType(['bar' => new IntegerType()], ['bar']),
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			TrinaryLogic::createMaybe(),
+		];
+
+		// Optional property with incompatible types
+		yield [
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			new ObjectShapeType(['foo' => new StringType()], ['foo']),
+			TrinaryLogic::createMaybe(),
+		];
+
+		// Superset has extra required property - maybe because shapes are open
+		yield [
+			new ObjectShapeType(['foo' => new IntegerType(), 'bar' => new StringType()], []),
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			TrinaryLogic::createMaybe(),
+		];
+
+		// Subset is supertype
+		yield [
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			new ObjectShapeType(['foo' => new IntegerType(), 'bar' => new StringType()], []),
+			TrinaryLogic::createYes(),
+		];
+
+		// Empty shape is supertype of any shape
+		yield [
+			new ObjectShapeType([], []),
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			TrinaryLogic::createYes(),
+		];
+
+		// Any shape is maybe supertype of empty shape
+		yield [
+			new ObjectShapeType(['foo' => new IntegerType()], []),
+			new ObjectShapeType([], []),
+			TrinaryLogic::createMaybe(),
+		];
+	}
+
+	#[DataProvider('dataIsSuperTypeOf')]
+	public function testIsSuperTypeOf(ObjectShapeType $type, Type $otherType, TrinaryLogic $expectedResult): void
+	{
+		$actualResult = $type->isSuperTypeOf($otherType);
+		$this->assertSame(
+			$expectedResult->describe(),
+			$actualResult->describe(),
+			sprintf('%s -> isSuperTypeOf(%s)', $type->describe(VerbosityLevel::precise()), $otherType->describe(VerbosityLevel::precise())),
+		);
+	}
+
+}
diff --git a/tests/PHPStan/Type/TypeCombinatorTest.php b/tests/PHPStan/Type/TypeCombinatorTest.php
index 6c51dbcd9b..7e6557a493 100644
--- a/tests/PHPStan/Type/TypeCombinatorTest.php
+++ b/tests/PHPStan/Type/TypeCombinatorTest.php
@@ -2578,6 +2578,54 @@ public static function dataUnion(): iterable
 			UnionType::class,
 			'object{bar: string}|object{foo: int}',
 		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+				new ObjectShapeType(['foo' => new IntegerType()], ['foo']),
+			],
+			ObjectShapeType::class,
+			'object{foo?: int}',
+		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+				new ObjectShapeType(['foo' => TypeCombinator::union(new IntegerType(), new NullType())], []),
+			],
+			ObjectShapeType::class,
+			'object{foo: int|null}',
+		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+				new ObjectShapeType(['foo' => TypeCombinator::union(new IntegerType(), new NullType())], ['foo']),
+			],
+			ObjectShapeType::class,
+			'object{foo?: int|null}',
+		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+				new ObjectShapeType(['bar' => new IntegerType()], ['bar']),
+			],
+			UnionType::class,
+			'object{bar?: int}|object{foo: int}',
+		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+				new ObjectShapeType(['foo' => new StringType()], ['foo']),
+			],
+			UnionType::class,
+			'object{foo: int}|object{foo?: string}',
+		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType(), 'bar' => new StringType()], []),
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+			],
+			ObjectShapeType::class,
+			'object{foo: int}',
+		];
 
 		yield [
 			[
@@ -4584,8 +4632,8 @@ public static function dataIntersect(): iterable
 				new ObjectShapeType(['foo' => new IntegerType()], []),
 				new HasPropertyType('bar'),
 			],
-			NeverType::class,
-			'*NEVER*=implicit',
+			ObjectShapeType::class,
+			'object{bar: mixed, foo: int}',
 		];
 		yield [
 			[
@@ -4616,9 +4664,73 @@ public static function dataIntersect(): iterable
 				new ObjectShapeType(['foo' => new IntegerType()], []),
 				new ObjectShapeType(['bar' => new StringType()], []),
 			],
+			ObjectShapeType::class,
+			'object{bar: string, foo: int}',
+		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+				new ObjectShapeType(['foo' => new IntegerType()], ['foo']),
+			],
+			ObjectShapeType::class,
+			'object{foo: int}',
+		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+				new ObjectShapeType(['foo' => TypeCombinator::union(new IntegerType(), new NullType())], []),
+			],
+			ObjectShapeType::class,
+			'object{foo: int}',
+		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+				new ObjectShapeType(['foo' => TypeCombinator::union(new IntegerType(), new NullType())], ['foo']),
+			],
+			ObjectShapeType::class,
+			'object{foo: int}',
+		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+				new ObjectShapeType(['bar' => new IntegerType()], ['bar']),
+			],
+			ObjectShapeType::class,
+			'object{bar?: int, foo: int}',
+		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+				new ObjectShapeType(['foo' => new StringType()], ['foo']),
+			],
 			NeverType::class,
 			'*NEVER*=implicit',
 		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], ['foo']),
+				new ObjectShapeType(['foo' => new StringType()], ['foo']),
+			],
+			ObjectShapeType::class,
+			'object{}',
+		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType()], ['foo']),
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+			],
+			ObjectShapeType::class,
+			'object{foo: int}',
+		];
+		yield [
+			[
+				new ObjectShapeType(['foo' => new IntegerType(), 'bar' => new StringType()], ['foo']),
+				new ObjectShapeType(['foo' => new IntegerType()], []),
+			],
+			ObjectShapeType::class,
+			'object{bar: string, foo: int}',
+		];
 		yield [
 			[
 				new ObjectShapeType(['foo' => new IntegerType()], []),