There is no third playthrough, only 2. Once you beat the second time through you can go back and keep playing on it and keep killing all the bosses but your not going to get missions to play or anything like that.
What about playthrough 2.5?
Playthrough 2.5 is when you finish the 2nd playthrough. The enemies will be lvl 50 or 51(Badass enemies, Bully,etc) The drops and the items on chest will always be lvl 48 (lvl 49 only on Eridian weapons) But then again, there's no missions anymore.