It is widely believed that eco-evolutionary feedbacks arising from host-pathogen interactions shape the number and frequency of resistance (R) genotypes and the allelic polymorphism that they harbor. A subset of R genes exhibit unusually strong signatures of balancing selection, sometimes even existing as trans-specific polymorphism. Here, we explore the role of alternative hosts on R gene evolution through a simple model of two closely related host species that share a single generalist pathogen. We ask (i) how shared interactions determine the R gene repertoires and polymorphism in each host and (ii) under which circumstances trans-specific polymorphism is maintained. Our results indicate that interactions with a generalist pathogen are more likely to sustain polymorphism at a shared ancestral R gene compared to the maintenance of polymorphism at R genes private to each host. The former often translates into trans-specific resistance gene polymorphism. Further, we observe that increasing the relative proportion of a single host species favors fixation of private resistance in the less common host, as the pathogen tracks the more common host. Thus, our model sheds light on how R gene dynamics are shaped by interactions with a shared generalist pathogen and the pathogen\'s response to unequal host frequencies.