Diversity of social identities can improve the performance of groups through varied cognitive and communicative pathways. Recently, research efforts have focused on identifying when we should expect to see these potential benefits in real-world settings. While most research to date has studied this topic at individual and interpersonal levels, in this paper, we develop an agent-based model to explore how various aspects of homophily, the tendency of individuals to associate with similar others, affects performance at a larger scale. Study 1 (...) examines how two types of homophily---identity-driven and opinion-driven---impact collective performance on a sequential decision-making task via modulating network formation and trust relations. Study 2 considers how the presence of identity-based conformity pressure can affect the findings from the first study. Overall, we find that the effect of homophily on performance is complex, depending on the operative dimensions of similarity, mediating pathways, and the specific outcome of interest. Finally, we discuss the implications of our results for policy interventions aiming to improve group performance. (shrink)