Funny, because JJ's universe is already an alternate timeline (or an alternate universe altogether, depending on who you listen to), so we now have at least four universes.
The Prime universe
The Mirror Mirror universe
The Abrams Mirror verse
Not to mention the countless universes we've seen in other episodes, notably Parallels in TNG. Perhaps in one Mirror universe, the Klingon/Cardassian alliance has cloaking devices (Crossover), and in another, they do not (The Emperors New Cloak)