I'm not sure about the grammar rules, but I would say that no, you don't hear people saying "more higher". You can say high/higher/highest. Maybe you can say "more high", but I can't think of a context when you would use it. Do you have an example sentence that you would use the words "more higher"?

only "higher"

Higher :) "more higher" does not sound right.

Higher!

Only "higher" is correct.