Combination Platter tells the story of a Chinese restaurant in the New York City area and its employees. One of these workers is Robert, an illegal immigrant, who is desperately seeking a green card. His best route to attain this goal, he admits, is to marry an American woman. When an attempt to offer $25,000 to a Chinese-American woman in exchange for marriage fails, he reluctantly agrees to meet an Anglo-American woman, Claire. Thus, there are scenes of the dating couple intermingled with real-to-life scenarios from the restaurant. The viewer glimpses interesting and irate customers, after work gatherings, kitchen mayhem and more. But, will Robert attain residency in this country before the Immigration service catches up to him?