A ternary fluid mixture, in which molecular pairs of like species have no interaction and molecular pairs of unlike species interact as hard spheres, is studied in a mean-field approximation., As the pressure is raised the system passes from a state of complete miscibility to states with 3 bicritical points, to a state with 3 tricritical points, to states with 6 bicritical points, to a state with a quadruple point, and finally to states of almost total mutual immiscibility. The behaviour near a tricritical point is discussed in detail, and the system compared briefly with a lattice model—the 3-states Potts model.