Turn based MP? It would be a departure from the mechanics (in the OTHER direction than what I discussed earlier), but in addition to that, I just don't think those who want MP badly enough to affect their purchasing decision would be content with a turn-based mode.
Turn Based MP would be a departure from the core mechanics in place for SP its true, although I would still see it as a viable selling point for players interested in MP.
One of my favorite MP turn based RPGs growing up was the Lucasarts video game Gladius for the original Xbox, and Nitendo Gamecube consoles. The game would allow up to four players to control various gladiators during the fights; now one could simply have passed one controller around and called it MP but there was something about having four people sitting around the TV, each with their own character(s), and planning out their actions that made the game engaging. The local, drop in/drop out MP was available for the SP campaign as well as a vs mode that could be played on arenas unlocked in SP.
Gladius was made even more engaging thanks to the fact that players could recruit the exotic creatures into their party; things like Yeti, Ogres, Minotaurs, Saytrs, Wolves, Big Cats, giant scorpions and beetles, walking skeletons in addition to the standard human warriors, archers/rogues, and casters, and that each of those party members were playable in MP.
Man, now I really wish that Gladius had (or will get) a sequel 
Other games like Operation: Darkness, or the recent X-COM, and the possible/rumored MP expansion to Shadowrun Returns, also have (have the potential to have) unique MP experiences that are rare among the more 'fast paced' MP games/modes flooding the market nowadays.