In spectroscopy, is it possible for the sample to be excited multiple times?
Very technically? Yes.

Realistically? The probability is small enough that even if it does happen, the peaks for the multiple transitions are going to be small enough that we cannot really observe them on the spectrum. The lifetime of a given excited state is so small compared to the analogous time in the ground state that it can basically be considered zero for the situation you're talking about. I'm sure it has happened, but compared to the one at a time transitions, your spectrum isn't really going to show it.