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you may have to self-transfer on this flight. read about it below.
Japan Airlines via Skyscanner have round trip airfares travelling from New York (JFK) to Kaohsiung Taiwan (KHH) for $ 751-$ 786, making 1 stop in Tokyo. Be sure you book this deal, make sure you’re okay with self-transfer but I think it will be okay since there’s enough time.
Travel Availability:
Departs JFK: Oct 1-2, 7-10, 14-17, 21-24, 28-31; Nov 12-13, 19
Returns: wide availability returns on 7, 8, 9, 14-day stays