A key aim in the dynamics and control of infectious diseases is predicting competitive outcomes of pathogen interactions. Observed pathogen community structure indicates both considerable coexistence of related variants and spectacular instances of replacement, notably in seasonal influenza and SARS-CoV-2. However, an overall comparative quantitative framework for invasion and coexistence remains elusive. Inspired by modern ecological coexistence theory, we address this gap by developing pathogen invasion theory (PIT) and test the resulting framework against empirical systems. PIT predicts near-universal mutual invasibility across major pathogen systems, including seasonal influenza strains and SARS-CoV-2 variants. Predicting co-circulation from mutual invasibility further depends on the extent of overcompensatory susceptible depletion dynamics. Our analyses highlight the central role of immuno-epidemiological factors in determining pathogen coexistence and community structure.