assertEquals(user2, chain.updateCalls.get(1));
        assertEquals(user3, chain.updateCalls.get(2));
    }

    // Test update with exception handling
    @Test
    public void test_update_withException() {
        TestAuthenticationChain chain = new TestAuthenticationChain();
        chain.updateThrowsException = true;
        User user = createTestUser("testuser", "Test User");

        try {