Extensive theory has been developed for the interactions between predators and their prey. However, the majority of existing theory focuses on predators which specialize on a single prey species, though most predators in nature are generalists, feeding upon multiple prey species. Furthermore, a large body of evidence suggests that generalist predator populations are heterogeneous, comprised of individuals that vary from being specialists on a single prey species to generalists that feed across multiple prey species. Therefore, theory is required that accounts for both the generality of a predator at the population level and the heterogeneity among predators at the individual level. Here I present a mathematical model of a one predator-two prey system in which the predator population is compartmentalized into three sub-populations: one that is a generalist on both prey species and two sub-populations that are specialists each on one of the alternative prey species. I present a preliminary numerical analysis of the dynamics of the system assuming a variety of possible functions for distributing predators among the three compartments. I then discuss the possible ramifications of this theory for our understanding of predator-prey dynamics and the stability of predator-prey interactions.