We consider a generalization of the standard Potts model in which there are q=r+s states with an interaction that distinguishes the two subspecies. We develop a graphical representation (of the FK type) for the system and show that this representation may be incorporated directly into reflection positivity arguments. Using combinations of these techniques, we establish detailed properties of the phase diagram including the existence of sharp triple points. Whenever relevant, the phases are characterized by the percolation properties of the underlying representation.