Although host-parasite models have been widely studied, the inclusion of predators has often been overlooked until recently. In this study, we examine a host-parasite model with a predator and show that the predator changes the stability and increases branching possibilities. We find that the hosts maximize their levels of resistance at intermediate predation rates, where the cost of infection is high due to the presence of infected hosts and predators. We show that the branching possibilities increase with the predation rate for regions where the susceptible and infected hosts co-exist with the predator. The results reveal the diversity that can be produced by the addition of predators to a population.