Can you change tenses per paragraph?

It depends on what you're writing. If you're writing a novel then it's a common technique for writer's to change tense. For example, if you are primarily writing in present tense, you could switch to past tense when talking about something that happened previously.

If you are writing something academic (such as an essay or thesis) then you should try to remain consistent with your tense and not switch.

Changing your tenses too often will confuse your reader so be careful.