Many pathogens have clusters of variation in their genotypes that we refer to as strain structure. Importantly, when considering related pathogen strains, host immunity to one strain is often neither independent from nor equivalent to immunity to other strains. This partial cross-reactive immunity can thus allow repeated infection with (different strains of) the same pathogen and affects disease dynamics across a population, influencing the effectiveness of intervention strategies. To better understand the dynamics governing multi-strain pathogens in complex landscapes, we combine two frameworks well-studied in their own right: multi-strain disease dynamics and metapopulation network structure. We simulate the dynamics of a multi-strain disease on a network of populations connected by movement, and characterize the joint effects of disease model parametrization and network structure on these dynamics. We find that the movement of (partially) immune individuals tends to have a larger impact than the movement of infectious individuals, dampening infection dynamics in populations further along a chain. Additionally, dynamics can propagate from one population to another, even if disease parameters vary between populations. In addition to providing novel insights into the role of host movement on disease dynamics, this work provides a framework for future predictive modelling of multi-strain diseases across generalized population structures.