diff --git a/src/Type/UnionType.php b/src/Type/UnionType.php
index 12f0d540ba..3388d0e4a0 100644
--- a/src/Type/UnionType.php
+++ b/src/Type/UnionType.php
@@ -1234,6 +1234,38 @@ public function inferTemplateTypes(Type $receivedType): TemplateTypeMap
 			$myTypes = $this->types;
 		}
 
+		// When every member of the union is a template type (e.g. T1|T2) and the received
+		// type only matches some of them, the unmatched template types cannot be inferred
+		// from this argument. Bind them to never so the union narrows to the matched members
+		// instead of widening each unmatched template to its bound.
+		if (count($myTypes) > 1) {
+			$templateMembers = [];
+			foreach ($myTypes as $type) {
+				if (!$type instanceof TemplateType) {
+					$templateMembers = [];
+					break;
+				}
+				$templateMembers[] = $type;
+			}
+
+			if (count($templateMembers) > 0) {
+				$matchedTypes = TemplateTypeMap::createEmpty();
+				$unmatchedNames = [];
+				foreach ($templateMembers as $type) {
+					$inferred = $type->inferTemplateTypes($receivedType);
+					if ($inferred->isEmpty()) {
+						$unmatchedNames[] = $type->getName();
+						continue;
+					}
+					$matchedTypes = $matchedTypes->union($inferred);
+				}
+
+				if (!$matchedTypes->isEmpty() && count($unmatchedNames) > 0) {
+					return $matchedTypes->union(new TemplateTypeMap(array_fill_keys($unmatchedNames, new NeverType(true))));
+				}
+			}
+		}
+
 		foreach ($myTypes as $type) {
 			if ($type instanceof TemplateType || ($type instanceof GenericClassStringType && $type->getGenericType() instanceof TemplateType)) {
 				continue;
diff --git a/tests/PHPStan/Analyser/nsrt/bug-2579.php b/tests/PHPStan/Analyser/nsrt/bug-2579.php
new file mode 100644
index 0000000000..f3572b4c4c
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-2579.php
@@ -0,0 +1,42 @@
+<?php declare(strict_types = 1);
+
+namespace Bug2579;
+
+use function PHPStan\Testing\assertType;
+
+class A {}
+class B {}
+class A1 extends A {}
+class B1 extends B {}
+
+/**
+ * @template T1 of A
+ * @template T2 of B
+ * @param T1|T2 $type
+ * @return T1|T2
+ */
+function f(object $type) {
+	return $type;
+}
+
+function test(): void
+{
+	assertType('Bug2579\\A1', f(new A1()));
+	assertType('Bug2579\\B1', f(new B1()));
+}
+
+/**
+ * @template T1 of A
+ * @template T2 of B
+ * @template T3 of \Countable
+ * @param T1|T2|T3 $type
+ * @return T1|T2|T3
+ */
+function g(object $type) {
+	return $type;
+}
+
+function test3(): void
+{
+	assertType('Bug2579\\A1', g(new A1()));
+}
diff --git a/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php b/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php
index a6e55ecbd3..9bcdb47767 100644
--- a/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php
+++ b/tests/PHPStan/Rules/Methods/CallMethodsRuleTest.php
@@ -987,6 +987,23 @@ public function testBug14720(): void
 		$this->analyse([__DIR__ . '/data/bug-14720.php'], []);
 	}
 
+	public function testBug2579(): void
+	{
+		$this->checkThisOnly = false;
+		$this->checkNullables = true;
+		$this->checkUnionTypes = true;
+		$this->analyse([__DIR__ . '/data/bug-2579.php'], [
+			[
+				'Call to an undefined method Bug2579Methods\A1::bar().',
+				30,
+			],
+			[
+				'Call to an undefined method Bug2579Methods\B1::foo().',
+				31,
+			],
+		]);
+	}
+
 	public function testClosureBind(): void
 	{
 		$this->checkThisOnly = false;
diff --git a/tests/PHPStan/Rules/Methods/data/bug-2579.php b/tests/PHPStan/Rules/Methods/data/bug-2579.php
new file mode 100644
index 0000000000..eafd8419b4
--- /dev/null
+++ b/tests/PHPStan/Rules/Methods/data/bug-2579.php
@@ -0,0 +1,32 @@
+<?php declare(strict_types = 1);
+
+namespace Bug2579Methods;
+
+class A {}
+class B {}
+class A1 extends A {
+	public function foo(): void {}
+}
+class B1 extends B {
+	public function bar(): void {}
+}
+
+/**
+ * @template T1 of A
+ * @template T2 of B
+ * @param T1|T2 $type
+ * @return T1|T2
+ */
+function f(object $type)
+{
+	return new $type();
+}
+
+function test(): void
+{
+	(f(new A1()))->foo(); // should pass
+	(f(new B1()))->bar(); // should pass
+
+	(f(new A1()))->bar(); // should fail
+	(f(new B1()))->foo(); // should fail
+}