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It occurs to me that a 3-player Besiege Chess with equal armies could very easily be achieved on a suitably adjusted board. One would be to have three FIDE arrays stuck together - Red v Yellow, Red v Blue, and Yellow v Blue, say, with one put in the middle and its camps joined to the same-colour ones on the other boards, and one King turned to a Queen for each player. If this looks too grotesquely large, another possibility is to join two boards but remove the file a/b/g/h squares from the middle 4 ranks. In the latter case I would recommend the middle army having the first move to make up for being attacked on two fronts by two armies each internally united.