Host-shifts, where pathogens jump from an ancestral host to a novel host, can be facilitated or impeded by standing variation in disease resistance, but only if resistance provides broad-spectrum general resistance against multiple pathogen species. Host resistance comes in many forms and includes both general resistance, as well as specific resistance, which may only be effective against a single pathogen species or even genotype. However, most evolutionary models consider only one of these forms of resistance, and we have less understanding of how these two forms of resistance evolve in tandem. Here, we develop a model that allows for the joint evolution of specific and general resistance and asks if the evolution of specific resistance drives a decrease in the evolution of general resistance. We also explore how these evolutionary outcomes affect the risk of foreign pathogen invasion and persistence. We show that in the presence of a single endemic pathogen, the two forms of resistance are strongly exclusionary. Critically, we find that specific resistance polymorphisms can prevent the evolution of general resistance, facilitating the invasion of foreign pathogens. We also show that specific resistance polymorphisms are a necessary condition for the successful establishment of foreign pathogens following invasion, as they prevent the exclusion of the foreign pathogen by the more transmissible endemic pathogen. Our results demonstrate the importance of considering the joint evolution of multiple forms of resistance when evaluating a population's susceptibility to foreign pathogens.