What if it is not a direct flight may I board a second plane on second day yom tov even though I am a ben haarets and only keep one day?

Shalom, Thank you for your question. It isn't clear to me the exact details of the situation you are going to be in. Perhaps you (an Israeli) are flying out of Israel after first day Yom Tov to go abroad. It sounds like your ultimate arrival at your destination will be after second day Yom Tov is over, however you will need to change flights on the way and this in-transit landing and take off will occur when it is still second day Yom Tov. If this is the case then there are major rabbinic opinions that allow it. This is because when in transit you stay in the airport which is considered similar to a "desert" – that is a place that does not yet obligate you to refrain from labor on second day Yom Tov (see the work Yom Tov Sheni BeHalacha, 3:11). If though you had to leave the airport (to say go to a different airport for the second flight, or stay overnight in a hotel etc) and entered a city with a Jewish community, then it would be forbidden, as even an Israeli is forbidden to perform forbidden labor on second day in a city with Jews in it, outside of Israel, and driving is certainly included in this. From the above it should be clear that if you are already in a city that has a Jewish community in it (and not just passing through the airport), it is forbidden to fly out of it on second day, for it would be forbidden to drive to the airport. I hope this answer your query. If you have any more questions, please feel free to send in a more detailed question, and we will be more than happy to answer it. Blessings.