There are in my experience no fun games for 12-14 people (Except Werewolf variants). I'd get a few different ones and split into groups of 2-3 instead - then everyone can play something to their taste as well.
Dominion is good, but as said DO NOT double up. Even at 5-6 as described in the rules it's boring as hell. 4 is max in my opinion for it to still be enjoyable.
King of Tokyo/New York is a nice quick game that I think would be excellent to bring along. Something like Zombiecide could also do very well, and it's co-op so could do well for those not enjoying conflict as much.
Spartacus I would not recommend personally - the rules as written are severely flawed (You will get combats where neither player does anything as it's suboptimal to allow the other player to strike first); and I personally absolutely detest its bribe mechanic (You can do it at any time for anything, only with gold though. It makes for very awkward and time wasting plays... like "Want to bribe me to avoid going into the arena? - Sure, have 2 gold, agreed? - Yeah, sure. *turns to next player* Want to bribe me to go into arena? - yeah, sounds good, 2 gold ok? - Yeah. *turn to first player* Guess what, you're going into the arena, vs the 4th player who refused to bribe me either way.) Just a waste of time to go through all the lying etc just to get your scemes through, and nothing is binding. Timings are very ambigious in the rules in regards to timing of cards played and bribes etc.
Twilight Imperium is pretty epic, and could do well if you have the right minded friends. I really like Chaos in the Old World otherwise for 4 players as it plays very quickly once learnt - usually takes 1-1½ hour with experienced players. Civilization the board game is also one of my real favorites.