Saturated square well (SSW) particles provide a model for atoms and molecules with valency in which the interparticle potential is not pairwise additive. The many-body constraints in the potential make it easier to calculate the third virial coefficient for the SSW models than for the simpler, pairwise additive, square well model. Fluid pressures predicted by the truncated virial equation are compared with simulation results to determine the density and temperature ranges over which the truncated series is accurate.