The coinfection of a host by several parasite strains is known to affect selective pressures on parasite strategies of host exploitation. I present a general model of coinfections that ties together kin selection models of virulence evolution and epidemiological models of multiple infections. I derive an analytical expression for the invasion fitness of a rare mutant in a population with an arbitrary distribution of the multiplicity of infection (MOI) across hosts. When a single mutation affects parasite strategies in all MOI classes, I show that the evolutionarily stable level of virulence depends on a demographic average of within-host relatedness across all host classes. This generalization of previous kin selection results requires that within-host parasite densities do not vary between hosts. When host exploitation strategies are allowed to vary across classes, I show that the strategy of host exploitation in a focal MOI class depends on the relative magnitudes of parasite reproductive values in the focal class and in the next. Thus, in contrast to previous findings, lower within-host relatedness in competitive parasite interactions can potentially correspond to either higher or lower levels of virulence.