I run Mage: the Awakening, so yes, personality is covered under game rules for PCs. And I've let him play a character with MPD before--he's currently playing one in another game, in fact, and that's a major reason why I don't want this new character for my Mage game. The character in that game single-handedly changed the tone of the game from "Victorian horror full of dread and intrigue" to "I try to charm the squirrel, because this personality is so random!" I adapted, and so the game has more light-hearted, goofy moments he engages in while the rest of the group goes about the business of being monster hunters in Victorian London.
Really, it's a matter of tone. Specifically, he wants his character to be the result of a magical accident in which a brother and sister were fused together in one body, and the guy becomes his sister at night. Yeah, it's a new take on MPD, and it would be pretty good for a Beer and Pretzels D&D game, but Mage just isn't that game. It's a game of modern horror, in which fairly normal human beings learn that there is an invisible world around them and become corrupted by their own hubris. I mean, can you think of a way to put that idea into the horror genre?
To me, it's like coming to a game of Call of Cthulhu with a character who wants to dual-wield katanas and wear a trench coat. Yeah, you can make the rules do that--but it's completely missing the point of Call of Cthulhu. In any game, there are some ideas that are just too far outside the tone of the game.