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Round two in contemplating a budgeted Extraction design. This time using U/B and cheap alternatives to the more traditional power cards, and is less extraction than it is an iso-toolbox with extraction, control, and removal as a theme. Word of Command is expensive, but if the deck works, I think it'd be worth it. Not before I invested in at least a pair of Mox Diamonds, though. Extirpate == Surgical Extraction from New Phyrexia.
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My main concern is that I think I might spend too much time setting up, and not enough time asserting control early game.
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I will warn you, you said this was for multiplayer....Extraction has a hard time in multiplayer. There's just much more to deal with and specifically, more to extract... Still, this deck does have a good design for the necessary versatility of multiplayer.
It's not that this was made for multiplayer, it's that I play a lot of multiplayer.. so the iso-toolbox design works well in that regard. Our multiplayer meta involves a lot of politicking. Provided I'm able to tutor, first card I'll grab is Propaganda (which I might add a second), as that completely kills players' battlefield advantage if they attack me, while other players can continue to build up. That should give me enough time to put a few more bargaining chips on the battlefield, but then victory itself will be a trickier matter, switching to the offense at the right time is vital. At the very least, if somebody goes all out against I should be able to cripple their libraries before they finish me off. And then I can still enjoy watching them suffer through the rest of the game :) Might not be the best theme for multiplayer, but I still think it will be fun as hell to play ^-^
Also, that post made me think to start designing a sideboard to better handle multiplayer games. Some cards (like Soul Conduit and Knowledge Pool) are just for shenanigans. Also just replaced Disperse with Boomerang so I can bounce lands as well.