Is it safe to take 3 Aleve at once?

It's not a good idea.

The real problem here is the aspirin/ibuprofen combination. You can normally mix acetaminophen with either of those things, but combining aspirin with NSAIDs is a no-no.

The other complicating factor is that "Tylenol 3" contains an opioid, codeine. I know that codeine and aspirin are sometimes combined, but you're adding acetaminophen to the mix as well, you should probably ask your pharmacist.