Earlier ideas that parasites evolve toward becoming harmless to their hosts have, in recent years, given way to more analytic studies, focused on the 'basic reproductive rate', R0, of individual parasites. In general, the biology of the parasite life cycle will lead to constraining relations between virulence (parasite-associated host death or reduction in fertility) and transmissibility: the maximum R0 may then be attained by virulence being high, or low, or at some intermediate level, depending on the details of the constraining relations. Such studies have not generally included superinfection (where an already-infected host is infected by another parasite). Here we propose a general, but simple, model of superinfection, which is amenable to analytical treatment. In such models selection does not simply act to maximize R0; superinfection leads to selection for higher levels of virulence, highly polymorphic parasite populations and very complicated dynamics. We calculate the equilibrium distribution of parasite strains and the maximum level of virulence that can be maintained by superinfection. We also note the equivalence between our 'superinfection model' and recent approaches to the study of the meta-population dynamics of multi-species interactions.