Chemistry - In spectroscopy, is it possible for the sample to be excited multiple times?

Solution 1:

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.

Solution 2:

From memory something like this has been used as a basis for isotope separation using intense $\ce{CO2}$ lasers to fragment molecules. A process of 'ladder climbing' takes place aided by the fact that the electric field of the laser is so intense that it can bring levels into resonance that would otherwise not be so. Hence ladder climbing is possible. Multi-photon effects should also occur.

Solution 3:

Multiple excitations are unlikely to occur incidentally (at least to the extent where you would get an appreciable signal), but I know of research groups that look at multiple excitations as a way of triggering reactions or as a means of studying excited states via pump-probe spectroscopy