When Yom Tov fell on Friday in the desert, did three times the normal amount of man fall on Thursday, to last through Shabbat? If so, does anyone discuss having three challot at meals on a Friday Yom Tov?
There is a Machlokes whether the Man fell on Yom Tov or not. The Gra in Hilchos Pesach discusses whether there should be 2 or 3 Matzos on the Ka'ara. According to the Rif since you do not need Lechem Mishna on Yom Tov, therefore even after you break the Matza at Yachatz you can still make Hamotzi on the remaining 1 1/2 Matzohs. (Rabbi Moshe Feinstein Zatzal also only used 2 Matzos at the Seder - per Artscroll Hagada based on Rabbi Moshe Feinstein Zatzal)
Even according to those that hold that you do need Lechem Mishna on Yom Tov the reason for Lechem Mishna on Shabbos is not because there were 2 breads for Shabbos, it is because double bread fell on Friday. To remember this miracle we have 2 breads on Shabbos. That 3 breads fell on a Thursday is not a change in the fact of the miracle.
My own reason not to use 3 is that Shabbos is more holy than Yom Tov and it is inappropriate to use 3 on Yom Tov when you only use 2 on Shabbos.