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No, because frequency is a fundamental quality of a wave. Things that are affected by one frequency could also be affected by another in certain cases (such as when two frequencies are integer multiples), but the waves themselves will never affect each other.
As an analogy, imagine playing a specific note on a flute. It doesn't matter how many other notes you play, that original note will always be there alongside the others.
Thanks for the analogy! It's pretty easy to understand how that works. I think I was imagining that EM waves shared some qualities with mechanical waves like sound, but I suppose that's not the case!