So, in a world of political intrigue, power plays, and greed; I imagine that this world would have multiple villains, but more importantly multiple villains in the same plot line.
How do multiple Villains that aren't beholden or loyal to each other work? I don't want to play both parties, because try as I might, it is still hard for me to evaluate the scenario through both villain eyes, without objectively knowing that the other villain was going to do. Example: Terry Benedict in Ocean's Thirteen, where he is clearly an antagonist who is in it for himself. While this example is perhaps less influential in the plot line, it still proves the story that I think that there could be two political forces that are neither aligned with the Heroes nor each other could exist.
A second example is the anime Lord Marksman and Vanadis. In it, two Dukes are vying for power and the throne as the King lays wasting away, and they both present obstacles to the protagonists.
What should I do? Should I just play both? Or could I have another person play the other Villain? This way it is both more representative of the clash between Villains, and that while I would not be privy to his interests and motivations, I could still monitor and be part of the Villain creation, as I would still be the GM.
I'm not really sure why this is any more difficult than any other game where you might pit multiple villains against the heroes? Does the secondary Villain have something at stake? Is there some goal he/she is trying to achieve? Then you invest Influence. If the heroes foil one plot and not the other, the unfoiled plot returns an influence bonus to that villain. If the heroes can manage to foil BOTH plots, neither villain achieves their ends and both go unrewarded. You don't really need to play out the scenario through the villain's eyes. Just answer those questions. If the answer to either one is yes, then there is an influence investment.
Here's a twist: it might be in a villain's interest to HELP the heroes foil another plot to achieve her own scheme.
I agree with Blu that there is no reason this should be any different than any other RPG with multiple villains. I would make the argument that, though you may have multiple "villain" types in your game, in any given story there should be one The villain. So, to use your analogy of Ocean's 13, Terry Benedict is indeed a villain, but Willy Bank is the villain.
It's fine to have multiple storylines going on simultaneously--it can give your players real choices to make--but a good story is going to have one main antagonist that the heroes face. Everyone else is essentially just playing a bit part.Sure, in the real world powerful parties are going to have their own schemes going on simultaneously, but the game isn't the real world. It is, however, a vehicle to tell a good story with your friends--everything else is secondary.
So, don't worry about inhabiting the mind of multiple "villains" with competing interests. Unless the point of your story is to make the heroes choose one over the other (who to side with, who to deal with first, who poses the greater threat and should be dealt with now vs. left for later, etc.), make a compelling, challenging villain, but one that your heroes can ultimately defeat. You'll be doing yourself, and them, a favor.