diff --git a/src/Type/Generic/TemplateTypeTrait.php b/src/Type/Generic/TemplateTypeTrait.php
index a1f381e6f5..aa6b5e17c0 100644
--- a/src/Type/Generic/TemplateTypeTrait.php
+++ b/src/Type/Generic/TemplateTypeTrait.php
@@ -18,6 +18,7 @@
 use PHPStan\Type\TypeUtils;
 use PHPStan\Type\UnionType;
 use PHPStan\Type\VerbosityLevel;
+use function count;
 use function sprintf;
 
 /**
@@ -287,6 +288,23 @@ public function inferTemplateTypes(Type $receivedType): TemplateTypeMap
 			]))->union($map);
 		}
 
+		if ($receivedType instanceof UnionType) {
+			$matchingTypes = [];
+			foreach ($receivedType->getTypes() as $innerType) {
+				if (!$resolvedBound->isSuperTypeOf($innerType)->yes()) {
+					continue;
+				}
+
+				$matchingTypes[] = $innerType;
+			}
+			if (count($matchingTypes) > 0) {
+				$filteredType = TypeCombinator::union(...$matchingTypes);
+				return (new TemplateTypeMap([
+					$this->name => $filteredType,
+				]))->union($map);
+			}
+		}
+
 		return $map;
 	}
 
diff --git a/tests/PHPStan/Rules/Methods/CallStaticMethodsRuleTest.php b/tests/PHPStan/Rules/Methods/CallStaticMethodsRuleTest.php
index 3ecba00c33..82ee7e1566 100644
--- a/tests/PHPStan/Rules/Methods/CallStaticMethodsRuleTest.php
+++ b/tests/PHPStan/Rules/Methods/CallStaticMethodsRuleTest.php
@@ -931,6 +931,38 @@ public function testBug13556(): void
 		$this->analyse([__DIR__ . '/data/bug-13556.php'], []);
 	}
 
+	public function testBug9732(): void
+	{
+		$this->checkThisOnly = false;
+		$this->checkExplicitMixed = true;
+		$this->checkImplicitMixed = true;
+
+		$this->analyse([__DIR__ . '/data/bug-9732.php'], [
+			[
+				'Parameter #1 $array of static method Bug9732\HelloWorld::stringifyKeys() expects array<string, mixed>, array<mixed> given.',
+				21,
+			],
+		]);
+	}
+
+	public function testBug12558(): void
+	{
+		$this->checkThisOnly = false;
+		$this->checkExplicitMixed = true;
+		$this->checkImplicitMixed = true;
+
+		$this->analyse([__DIR__ . '/data/bug-12558.php'], [
+			[
+				'Parameter #1 $object of static method Bug12558\Foo::assertStatic() expects Bug12558\Foo, Bug12558\Foo|null given.',
+				45,
+			],
+			[
+				'Parameter #1 $object of static method Bug12558\Foo::assertStatic() expects Bug12558\Foo, bool|Bug12558\Foo given.',
+				46,
+			],
+		]);
+	}
+
 	#[RequiresPhp('>= 8.5')]
 	public function testPipeOperator(): void
 	{
diff --git a/tests/PHPStan/Rules/Methods/data/bug-12558.php b/tests/PHPStan/Rules/Methods/data/bug-12558.php
new file mode 100644
index 0000000000..88a8224924
--- /dev/null
+++ b/tests/PHPStan/Rules/Methods/data/bug-12558.php
@@ -0,0 +1,48 @@
+<?php declare(strict_types = 1);
+
+namespace Bug12558;
+
+class Foo
+{
+	/**
+	 * @template T of object
+	 *
+	 * @param T $object
+	 *
+	 * @return (T is static ? T : static)
+	 */
+	public static function assertStatic(object $object)
+	{
+		if (!$object instanceof static) {
+			throw new \Error('Object is not an instance of static class');
+		}
+
+		return $object;
+	}
+
+	protected function createFoo(): self
+	{
+		return new Foo();
+	}
+
+	protected function createFooNullable(): ?self
+	{
+		return new Foo();
+	}
+
+	protected function createFooUnionedWithBool(): self|bool
+	{
+		return new Foo();
+	}
+
+	protected function foo(): void
+	{
+	}
+
+	public function testAssertInstanceOf(): void
+	{
+		(static::class)::assertStatic($this->createFoo())->foo();
+		(static::class)::assertStatic($this->createFooNullable())->foo();
+		(static::class)::assertStatic($this->createFooUnionedWithBool())->foo();
+	}
+}
diff --git a/tests/PHPStan/Rules/Methods/data/bug-9732.php b/tests/PHPStan/Rules/Methods/data/bug-9732.php
new file mode 100644
index 0000000000..292649803f
--- /dev/null
+++ b/tests/PHPStan/Rules/Methods/data/bug-9732.php
@@ -0,0 +1,23 @@
+<?php declare(strict_types = 1);
+
+namespace Bug9732;
+
+class HelloWorld
+{
+	/**
+	 * @phpstan-template TKeyType of string
+	 * @phpstan-template TValueType
+	 * @phpstan-param array<TKeyType, TValueType> $array
+	 * @phpstan-return \Generator<TKeyType, TValueType, void, void>
+	 */
+	public static function stringifyKeys(array $array) : \Generator{
+		foreach($array as $key => $value){
+			yield (string) $key => $value;
+		}
+	}
+
+	public function sayHello(): void
+	{
+		self::stringifyKeys($GLOBALS);
+	}
+}