Co-infection is an important aspect of many infectious diseases, with substantial modeling efforts in the last decades. Yet, simple and sufficiently general mathematical frameworks to analyze and unify the full spectrum of hierarchical patterns emerging from co-infection interactions and variation in other fitness dimensions between two or more strains are missing. Here, we contribute to fill this gap, thanks to a model reduction obtained after assuming strain similarity. We model simultaneously 5 fitness dimensions where strains can differ close to neutrality, and decompose dynamics in two timescales: neutral dynamics between types on a fast timescale, and non-neutral selective processes on a slow timescale, driven explicitly by trait variation and a replicator equation. We bridge adaptive dynamics and epidemiological multi-strain models, generalizing and advancing analytically these two perspectives on co-infection and coexistence.