Be very certain of your rationale for declaring this kind of thing… If you're just going off IP addresses, I know more than a few (creepy) married couples who can't get enough of playing Farmville and Mafia Wars together in bed.
Unless what the players are doing upsets some world-level game mechanic, like the amount of currency in the economy, it's just a lot of hassle to police them, and given the likelihood of false positives, can do a lot more marketing/community harm than good.
If your game requires a great deal of fair play, then you'll want to try filtering for what sort of players never cheat the system, then perhaps "shard" the bad players off to their own parallel game world, and set up a system that vets players for the "clean" world somehow. Even that will be gameable… But most other solutions are some level of annoying to the honest players, and should be avoided.
You'd also do well to read up on mmo/facebook game design post-mortems and interviews with the creators of similar games, and see how they dealt with issues like the one you're facing.
What should we do about obvious Facebook users who are exploiting our social game by playing with multiple accounts?