Electromagnetic EM waves - How they coexist in same space and time without signal impact?
The electrons will be excited by a superposition (sum) of the two EM waves. The waves will pass through each other much like waves on a pond. There is no differentiation between waves from different sources.

Occasionally it is possible to run in to nonlinearities that depend on the overall amplitude of the EM waves in question, and in this case all of the waves would be affected.