Parasite evolution is expected to modulate selective pressures acting upon host, and alter its response to infection. In such a context, parasite competition seems be a key variable for the evolutionary dynamics and epidemic features. We develop a nested coevolutionary model of host resistance and parasite virulence. From individual-based traits, we define a within-host model and derive from the within-host equilibrium the main epidemiological features of interest -transmission, virulence, recovery-. We use this first model to build an adaptive dynamics model in order to assess the joint evolution of the parasite virulence and host resistance. We compared the coevolutionarily stable states predicted by the model under different competition regimes, including single infections (preemption), superinfection (dominance) and coinfections (mixed). We find that parasite virulence under coinfections evolved towards higher values than under superinfections, while the opposite trend was observed for host resistance. The local coexistence of parasites enables a kin selection effects that reduce both virulence and the subsequent host response. We showed that the magnitude of multiple infections effects varies with the ecological context, and that the coevolutionary outcomes deviate from simple optimization of persistence depending on the degree of spatial coupling of hosts.