diff --git a/src/Type/ArrayType.php b/src/Type/ArrayType.php
index 7f3eed6f82..978e9d6ca8 100644
--- a/src/Type/ArrayType.php
+++ b/src/Type/ArrayType.php
@@ -493,7 +493,7 @@ public function intersectKeyArray(Type $otherArraysType): Type
 			return $this;
 		}
 
-		return new self($otherArraysType->getIterableKeyType(), $this->getIterableValueType());
+		return $this->withTypes($otherArraysType->getIterableKeyType(), $this->getIterableValueType());
 	}
 
 	public function popArray(): Type
@@ -533,7 +533,7 @@ public function sliceArray(Type $offsetType, Type $lengthType, TrinaryLogic $pre
 		}
 
 		if ($preserveKeys->no() && $this->keyType->isInteger()->yes()) {
-			return new IntersectionType([new self(IntegerRangeType::createAllGreaterThanOrEqualTo(0), $this->itemType), new AccessoryArrayListType()]);
+			return new IntersectionType([$this->withTypes(IntegerRangeType::createAllGreaterThanOrEqualTo(0), $this->itemType), new AccessoryArrayListType()]);
 		}
 
 		return $this;
@@ -561,7 +561,7 @@ public function spliceArray(Type $offsetType, Type $lengthType, Type $replacemen
 			return $type;
 		});
 
-		$arrayType = new self(
+		$arrayType = $this->withTypes(
 			TypeCombinator::union($keyType, $replacementArrayType->getKeysArray()->getIterableKeyType()),
 			TypeCombinator::union($this->getIterableValueType(), $replacementArrayType->getIterableValueType()),
 		);
@@ -591,12 +591,12 @@ public function makeListMaybe(): Type
 
 	public function mapValueType(callable $cb): Type
 	{
-		return new ArrayType($this->keyType, $cb($this->getItemType()));
+		return $this->withTypes($this->keyType, $cb($this->getItemType()));
 	}
 
 	public function mapKeyType(callable $cb): Type
 	{
-		return new ArrayType($cb($this->keyType), $this->getItemType());
+		return $this->withTypes($cb($this->keyType), $this->getItemType());
 	}
 
 	public function makeAllArrayKeysOptional(): Type
@@ -647,7 +647,7 @@ public function changeKeyCaseArray(?int $case): Type
 			return $type;
 		});
 
-		return new ArrayType($newKeyType, $this->getItemType());
+		return $this->withTypes($newKeyType, $this->getItemType());
 	}
 
 	public function filterArrayRemovingFalsey(): Type
@@ -658,7 +658,7 @@ public function filterArrayRemovingFalsey(): Type
 			return new ConstantArrayType([], []);
 		}
 
-		return new ArrayType($this->keyType, $valueType);
+		return $this->withTypes($this->keyType, $valueType);
 	}
 
 	private static function foldConstantStringKeyCase(ConstantStringType $type, ?int $case): Type
diff --git a/src/Type/IntersectionType.php b/src/Type/IntersectionType.php
index b65b75b274..56762ae30c 100644
--- a/src/Type/IntersectionType.php
+++ b/src/Type/IntersectionType.php
@@ -1151,7 +1151,11 @@ public function getKeysArray(): Type
 
 	public function getValuesArray(): Type
 	{
-		return $this->intersectTypes(static fn (Type $type): Type => $type->getValuesArray());
+		$cb = static fn (Type $type): Type => $type->getValuesArray();
+		if ($this->isList()->yes()) {
+			return $this;
+		}
+		return $this->intersectTypes($cb);
 	}
 
 	public function chunkArray(Type $lengthType, TrinaryLogic $preserveKeys): Type
@@ -1171,17 +1175,17 @@ public function flipArray(): Type
 
 	public function intersectKeyArray(Type $otherArraysType): Type
 	{
-		return $this->intersectTypes(static fn (Type $type): Type => $type->intersectKeyArray($otherArraysType));
+		return $this->intersectTypesPreserveTemplateType(static fn (Type $type): Type => $type->intersectKeyArray($otherArraysType));
 	}
 
 	public function popArray(): Type
 	{
-		return $this->intersectTypes(static fn (Type $type): Type => $type->popArray());
+		return $this->intersectTypesPreserveTemplateType(static fn (Type $type): Type => $type->popArray());
 	}
 
 	public function reverseArray(TrinaryLogic $preserveKeys): Type
 	{
-		return $this->intersectTypes(static fn (Type $type): Type => $type->reverseArray($preserveKeys));
+		return $this->intersectTypesPreserveTemplateType(static fn (Type $type): Type => $type->reverseArray($preserveKeys));
 	}
 
 	public function searchArray(Type $needleType, ?TrinaryLogic $strict = null): Type
@@ -1191,23 +1195,21 @@ public function searchArray(Type $needleType, ?TrinaryLogic $strict = null): Typ
 
 	public function shiftArray(): Type
 	{
-		return $this->intersectTypes(static fn (Type $type): Type => $type->shiftArray());
+		return $this->intersectTypesPreserveTemplateType(static fn (Type $type): Type => $type->shiftArray());
 	}
 
 	public function shuffleArray(): Type
 	{
-		$isList = $this->isList()->yes();
-		return $this->intersectTypes(static function (Type $type) use ($isList): Type {
-			if ($isList && $type instanceof TemplateType) {
-				return $type;
-			}
-			return $type->shuffleArray();
-		});
+		$cb = static fn (Type $type): Type => $type->shuffleArray();
+		if ($this->isList()->yes()) {
+			return $this->intersectTypesPreserveTemplateType($cb);
+		}
+		return $this->intersectTypes($cb);
 	}
 
 	public function sliceArray(Type $offsetType, Type $lengthType, TrinaryLogic $preserveKeys): Type
 	{
-		$result = $this->intersectTypes(static fn (Type $type): Type => $type->sliceArray($offsetType, $lengthType, $preserveKeys));
+		$result = $this->intersectTypesPreserveTemplateType(static fn (Type $type): Type => $type->sliceArray($offsetType, $lengthType, $preserveKeys));
 
 		if (
 			$this->isList()->yes()
@@ -1223,7 +1225,7 @@ public function sliceArray(Type $offsetType, Type $lengthType, TrinaryLogic $pre
 
 	public function spliceArray(Type $offsetType, Type $lengthType, Type $replacementType): Type
 	{
-		return $this->intersectTypes(static fn (Type $type): Type => $type->spliceArray($offsetType, $lengthType, $replacementType));
+		return $this->intersectTypesPreserveTemplateType(static fn (Type $type): Type => $type->spliceArray($offsetType, $lengthType, $replacementType));
 	}
 
 	public function makeListMaybe(): Type
@@ -1233,12 +1235,12 @@ public function makeListMaybe(): Type
 
 	public function mapValueType(callable $cb): Type
 	{
-		return $this->intersectTypes(static fn (Type $type): Type => $type->mapValueType($cb));
+		return $this->intersectTypesPreserveTemplateType(static fn (Type $type): Type => $type->mapValueType($cb));
 	}
 
 	public function mapKeyType(callable $cb): Type
 	{
-		return $this->intersectTypes(static fn (Type $type): Type => $type->mapKeyType($cb));
+		return $this->intersectTypesPreserveTemplateType(static fn (Type $type): Type => $type->mapKeyType($cb));
 	}
 
 	public function makeAllArrayKeysOptional(): Type
@@ -1248,12 +1250,12 @@ public function makeAllArrayKeysOptional(): Type
 
 	public function changeKeyCaseArray(?int $case): Type
 	{
-		return $this->intersectTypes(static fn (Type $type): Type => $type->changeKeyCaseArray($case));
+		return $this->intersectTypesPreserveTemplateType(static fn (Type $type): Type => $type->changeKeyCaseArray($case));
 	}
 
 	public function filterArrayRemovingFalsey(): Type
 	{
-		return $this->intersectTypes(static fn (Type $type): Type => $type->filterArrayRemovingFalsey());
+		return $this->intersectTypesPreserveTemplateType(static fn (Type $type): Type => $type->filterArrayRemovingFalsey());
 	}
 
 	public function getEnumCases(): array
@@ -1714,6 +1716,19 @@ private function intersectTypes(callable $getType): Type
 		return $result;
 	}
 
+	/**
+	 * @param callable(Type $type): Type $getType
+	 */
+	private function intersectTypesPreserveTemplateType(callable $getType): Type
+	{
+		return $this->intersectTypes(static function (Type $type) use ($getType): Type {
+			if ($type instanceof TemplateType) {
+				return $type;
+			}
+			return $getType($type);
+		});
+	}
+
 	public function toPhpDocNode(): TypeNode
 	{
 		$baseTypes = [];
diff --git a/tests/PHPStan/Analyser/nsrt/bug-14633.php b/tests/PHPStan/Analyser/nsrt/bug-14633.php
new file mode 100644
index 0000000000..6c2f3a6a8c
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-14633.php
@@ -0,0 +1,180 @@
+<?php declare(strict_types=1);
+
+namespace Bug14633;
+
+use function PHPStan\Testing\assertType;
+
+/**
+ * Tests for IntersectionType preserving TemplateType in array methods.
+ * Pattern: @template T with T&list<V> or T&array<K,V>
+ */
+class IntersectionTemplatePreservation
+{
+
+	/**
+	 * @template T
+	 * @param T&list<int> $items
+	 */
+	public function popList(array $items): void
+	{
+		array_pop($items);
+		assertType('list<int>&T (method Bug14633\IntersectionTemplatePreservation::popList(), argument)', $items);
+	}
+
+	/**
+	 * @template T
+	 * @param T&array<string, int> $items
+	 */
+	public function popArray(array $items): void
+	{
+		array_pop($items);
+		assertType('array<string, int>&T (method Bug14633\IntersectionTemplatePreservation::popArray(), argument)', $items);
+	}
+
+	/**
+	 * @template T
+	 * @param T&list<int> $items
+	 */
+	public function shiftList(array $items): void
+	{
+		array_shift($items);
+		assertType('list<int>&T (method Bug14633\IntersectionTemplatePreservation::shiftList(), argument)', $items);
+	}
+
+	/**
+	 * @template T
+	 * @param T&array<string, int> $items
+	 */
+	public function shiftArray(array $items): void
+	{
+		array_shift($items);
+		assertType('array<string, int>&T (method Bug14633\IntersectionTemplatePreservation::shiftArray(), argument)', $items);
+	}
+
+	/**
+	 * @template T
+	 * @param T&list<int> $items
+	 */
+	public function reverseList(array $items): void
+	{
+		$reversed = array_reverse($items);
+		assertType('list<int>&T (method Bug14633\IntersectionTemplatePreservation::reverseList(), argument)', $reversed);
+	}
+
+	/**
+	 * @template T
+	 * @param T&array<string, int> $items
+	 */
+	public function reverseArrayPreserveKeys(array $items): void
+	{
+		$reversed = array_reverse($items, true);
+		assertType('array<string, int>&T (method Bug14633\IntersectionTemplatePreservation::reverseArrayPreserveKeys(), argument)', $reversed);
+	}
+
+	/**
+	 * @template T
+	 * @param T&list<int> $items
+	 */
+	public function sliceList(array $items): void
+	{
+		$sliced = array_slice($items, 1);
+		assertType('list<int>&T (method Bug14633\IntersectionTemplatePreservation::sliceList(), argument)', $sliced);
+	}
+
+	/**
+	 * @template T
+	 * @param T&array<string, int> $items
+	 */
+	public function sliceArrayPreserveKeys(array $items): void
+	{
+		$sliced = array_slice($items, 0, 5, true);
+		assertType('array<string, int>&T (method Bug14633\IntersectionTemplatePreservation::sliceArrayPreserveKeys(), argument)', $sliced);
+	}
+
+	/**
+	 * @template T
+	 * @param T&list<int> $items
+	 */
+	public function arrayValuesOnList(array $items): void
+	{
+		$values = array_values($items);
+		assertType('list<int>&T (method Bug14633\IntersectionTemplatePreservation::arrayValuesOnList(), argument)', $values);
+	}
+
+	/**
+	 * array_values() on a non-list must NOT preserve T — keys change from string to int.
+	 *
+	 * @template T
+	 * @param T&array<string, int> $items
+	 */
+	public function arrayValuesOnNonList(array $items): void
+	{
+		$values = array_values($items);
+		assertType('list<int>', $values);
+	}
+
+	/**
+	 * shuffle() on a list preserves T — keys are already sequential integers.
+	 *
+	 * @template T
+	 * @param T&list<int> $items
+	 */
+	public function shuffleOnList(array $items): void
+	{
+		shuffle($items);
+		assertType('list<int>&T (method Bug14633\IntersectionTemplatePreservation::shuffleOnList(), argument)', $items);
+	}
+
+	/**
+	 * shuffle() on a non-list must NOT preserve T — keys change from string to int.
+	 *
+	 * @template T
+	 * @param T&array<string, int> $items
+	 */
+	public function shuffleOnNonList(array $items): void
+	{
+		shuffle($items);
+		assertType('list<int>', $items);
+	}
+
+}
+
+/**
+ * Tests for ArrayType methods preserving template via $this->withTypes().
+ * Pattern: @template T of array<K,V>
+ */
+class ArrayTypeTemplatePreservation
+{
+
+	/**
+	 * @template T of array<string, int>
+	 * @param T $items
+	 */
+	public function filterArrayRemovingFalsey(array $items): void
+	{
+		$result = array_filter($items);
+		assertType('T of array<string, int<min, -1>|int<1, max>> (method Bug14633\ArrayTypeTemplatePreservation::filterArrayRemovingFalsey(), argument)', $result);
+	}
+
+	/**
+	 * @template T of array<string, int>
+	 * @param T $items
+	 * @param array<string, mixed> $other
+	 */
+	public function intersectKeyArray(array $items, array $other): void
+	{
+		$result = array_intersect_key($items, $other);
+		assertType('T of array<string, int> (method Bug14633\ArrayTypeTemplatePreservation::intersectKeyArray(), argument)', $result);
+	}
+
+	/**
+	 * @template T of array<int, int>
+	 * @param T $items
+	 */
+	public function sliceArray(array $items): void
+	{
+		$result = array_slice($items, 1);
+		assertType('T of array<int<0, max>, int> (method Bug14633\ArrayTypeTemplatePreservation::sliceArray(), argument)&list', $result);
+	}
+
+}