Can you use the 毎X毎X pattern (indicating emphasis) for anything that would take 毎X? Circumstantial evidence suggests this should work: 毎日毎日 is clearly a thing, this post uses 毎晩毎晩, so one would assume it generalizes - but it doesn't hurt to be sure!
Yes, you can say 毎日毎日, 毎朝毎朝, 毎晩毎晩, 毎度毎度, 毎回毎回, 毎週毎週, and even 毎学期毎学期, 毎ターン毎ターン, 毎セット毎セット and so on.
Basically these are emphatic versions, but note that this pattern usually has a negative overtone, like the speaker is irritated by or bored of the repetition. For example, 毎日毎日練習して上達したいです sounds a little unnatural to me.