Shadow President, if you want to be the kind of president that takes over the world, and live up to the "Conspiracy Theorist/Tin Foil Hats Was Right" visage.
On that note, why aren't there any games where you get to play as a secret world power like the Illuminati, Freemasons, 4th Reich, or Scientology or whatever? Are they so scared of such a game potentially being accurate about their motives or something (the conspiracy source, not the developers; though it would be funny to see who reacts to such a game development. Who reacts could be one of Them.)?
You'd think they'd learn by now that it is possible to take refuge in audacity. The less serious you're taken, the easier it is to hide your true power (depending on what powers you possess). Like being the weird kid in school, which also happens to be in cahoots with the school board, and is actually far more rational than the popular kids pick on them for being the opposite of, or something. For all you know, they could be pretending to be autistic and anti-social, and you're playing right into their hands flawlessly (more powerful than the most influential people/populars). The best place for great power to hide is in plain sight.
Oh, there is, absolutely. I'm fairly sure it was coded by the dinosaur programmers from an antideluvian civilization (god, '92 seems so distant now...), but Floor 13 is just that. You're playing as a director of the British equivalent of the tinfoil hatter's Men In Black (operating, amusingly, from the Department of Fisheries of the Ministry of Agriculture, similar to how Secret Service used to be part of Treasury), preventing various nasty little scandals from discrediting the current government via more or less subtle measures, up to black ops raids or causing 'accidents'.
I didn't get that far, but apparently a while into the game various secret societies may recruit you, in fact.
Pretty interesting game, the horror of the world is hidden behind a wall of bureaucracy, so it's sorta a spiritual predecessor to Papers Please. Also I literally just learned someone's remaking it.
Well, also, again, LCS is pretty much that, after the earlygame, pretty much the exact picture of what conspiracy theorists imagine TEH LIBRULS are up to, complete with underhanded media takeovers, sleeper agents everywhere...
There's also that game where you play as the rogue AI spreading around the planet, where you buy out servers and hideout, can't recall the name, although it's only tangentially this.