diff --git a/src/Type/TypeCombinator.php b/src/Type/TypeCombinator.php
index d3442f0470..e7a0d6bdf5 100644
--- a/src/Type/TypeCombinator.php
+++ b/src/Type/TypeCombinator.php
@@ -1212,7 +1212,7 @@ public static function intersect(Type ...$types): Type
 		for ($i = 0; $i < $typesCount; $i++) {
 			$type = $types[$i];
 
-			if ($type instanceof IntersectionType) {
+			if ($type instanceof IntersectionType && !$type instanceof TemplateType) {
 				// transform A & (B & C) to A & B & C
 				array_splice($types, $i--, 1, $type->getTypes());
 				$typesCount = count($types);
diff --git a/tests/PHPStan/Analyser/nsrt/bug-13577.php b/tests/PHPStan/Analyser/nsrt/bug-13577.php
new file mode 100644
index 0000000000..2406bd0f95
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-13577.php
@@ -0,0 +1,35 @@
+<?php declare(strict_types = 1);
+
+namespace Bug13577;
+
+use function PHPStan\Testing\assertType;
+
+class A {}
+interface B {}
+
+/**
+ * @template T of A&B
+ */
+class Foo
+{
+	/**
+	 * @param T $foo
+	 */
+	public function a($foo): void
+	{
+		assertType('T of Bug13577\A&Bug13577\B (class Bug13577\Foo, argument)', $foo);
+
+		if (!$foo instanceof B) {
+			throw new \Exception();
+		}
+
+		assertType('T of Bug13577\A&Bug13577\B (class Bug13577\Foo, argument)', $foo);
+
+		$this->b($foo);
+	}
+
+	/**
+	 * @param T $foo
+	 */
+	public function b($foo): void {}
+}
diff --git a/tests/PHPStan/Analyser/nsrt/bug-14348.php b/tests/PHPStan/Analyser/nsrt/bug-14348.php
new file mode 100644
index 0000000000..b0e728ea8d
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-14348.php
@@ -0,0 +1,23 @@
+<?php declare(strict_types = 1);
+
+namespace Bug14348;
+
+use function PHPStan\Testing\assertType;
+
+interface PositionEntityInterface {
+	public function getPosition(): int;
+}
+interface TgEntityInterface {}
+
+abstract class HelloWorld
+{
+	/**
+	 * @phpstan-template T of PositionEntityInterface&TgEntityInterface
+	 *
+	 * @param non-empty-array<T> $tgs
+	 */
+	public function computeForFrontByPosition(array $tgs): void
+	{
+		assertType('T of Bug14348\PositionEntityInterface&Bug14348\TgEntityInterface (method Bug14348\HelloWorld::computeForFrontByPosition(), argument)', $tgs[0]);
+	}
+}
diff --git a/tests/PHPStan/Analyser/nsrt/bug-9961.php b/tests/PHPStan/Analyser/nsrt/bug-9961.php
new file mode 100644
index 0000000000..0e3535ee27
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-9961.php
@@ -0,0 +1,35 @@
+<?php declare(strict_types = 1);
+
+namespace Bug9961;
+
+use function PHPStan\Testing\assertType;
+
+interface Ia {}
+interface Ib {}
+interface Ic {}
+interface Id {}
+
+class A implements Ia, Ib {}
+
+class HelloWorld
+{
+	/**
+	 * @template T of (Ia&Ib)|(Ic&Id)
+	 * @param T $a
+	 * @return T
+	 */
+	public function sayHello(Ia|Ic $a): mixed
+	{
+		if ($a instanceof Ic && $a instanceof Id) {
+			assertType('T of Bug9961\Ic&Bug9961\Id (method Bug9961\HelloWorld::sayHello(), argument)', $a);
+		} elseif ($a instanceof A) {
+			assertType('Bug9961\A&T of T of Bug9961\Ia&Bug9961\Ib (method Bug9961\HelloWorld::sayHello(), argument) (method Bug9961\HelloWorld::sayHello(), argument)', $a);
+		} else {
+			throw new \Exception;
+		}
+
+		assertType('(Bug9961\A&T of T of Bug9961\Ia&Bug9961\Ib (method Bug9961\HelloWorld::sayHello(), argument) (method Bug9961\HelloWorld::sayHello(), argument))|T of Bug9961\Ic&Bug9961\Id (method Bug9961\HelloWorld::sayHello(), argument)', $a);
+
+		return $a;
+	}
+}
diff --git a/tests/PHPStan/Type/TypeCombinatorTest.php b/tests/PHPStan/Type/TypeCombinatorTest.php
index 9e4ab69709..6c51dbcd9b 100644
--- a/tests/PHPStan/Type/TypeCombinatorTest.php
+++ b/tests/PHPStan/Type/TypeCombinatorTest.php
@@ -42,6 +42,7 @@
 use PHPStan\Type\Generic\GenericObjectType;
 use PHPStan\Type\Generic\GenericStaticType;
 use PHPStan\Type\Generic\TemplateBenevolentUnionType;
+use PHPStan\Type\Generic\TemplateIntersectionType;
 use PHPStan\Type\Generic\TemplateMixedType;
 use PHPStan\Type\Generic\TemplateObjectType;
 use PHPStan\Type\Generic\TemplateObjectWithoutClassType;
@@ -4917,6 +4918,21 @@ public static function dataIntersect(): iterable
 			ObjectType::class,
 			$nonFinalClass->getDisplayName() . '=final',
 		];
+
+		// https://github.com/phpstan/phpstan/issues/14348
+		yield [
+			[
+				TemplateTypeFactory::create(
+					TemplateTypeScope::createWithFunction('a'),
+					'T',
+					new IntersectionType([new ObjectType('Iterator'), new ObjectType('Countable')]),
+					TemplateTypeVariance::createInvariant(),
+				),
+				new MixedType(),
+			],
+			TemplateIntersectionType::class,
+			'T of Countable&Iterator (function a(), parameter)',
+		];
 	}
 
 	/**