We have lechem mishne on Shabbos because a double portion of mon fell on Friday to make up for none falling on Shabbos. Tos (Beitzah 2) discusses whether mon fell on Y"T or not. Assuming it did not, Noda b'Yehudah asks why when Y"T falls on erev Shabbos (or on Sunday), lechem mishne suffices. Wouldn't a triple portion of mon have fallen, enough for Y"T + Shabbos, and therefore shouldn't we have to take 3 chalos?
Meshech Chochma in P' Beshalach answers that the point of having lechem mishne is to demonstrate the miracle of the mon not spoiling from erev Shabbos to the next day. It's the same miracle whether it was one day's extra worth of mon that did not spoil, or two days extra mon that did not spoil. Therefore, there is no need to increase the number of chalos that we use.
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