In terms of making a 'multi-player abstract perfect information game', territory is one of the more obvious themes because it is not mutually exclusive. Phalanx is such a game. However, Phalanx with more than two players thrives on over the board agreements, treaties and treason, in short, the kind of inherent diplomacy that disagrees with turnbased play. You'll have to make a fair number of base-3 boardsegments and get a lot of colored pieces if you want the multi-player experience. Here we cover only the two-player version.