Parasitic infections disturb gut microbial communities beyond their natural range of variation, possibly leading to dysbiosis. Yet it remains underappreciated that most infections are accompanied by one or more co-infections and their collective impact is largely unexplored. Here we developed a framework illustrating changes to the host gut microbiome following single infections, and build on it by describing the neutral, synergistic or antagonistic impacts on microbial α- and ß-diversity expected from co-infections. We tested the framework on microbiome data from a non-human primate population co-infected with helminths and Adenovirus, and matched patterns reported in published studies to the introduced framework. In this case study, α-diversity of co-infected Malagasy mouse lemurs (Microcebus griseorufus) did not differ in comparison with that of singly infected or uninfected individuals, even though community composition captured with ß-diversity metrices changed significantly. Explicitly, we record stochastic changes in dispersion, a sign of dysbiosis, following the Anna-Karenina principle rather than deterministic shifts in the microbial gut community. From the literature review and our case study, neutral and synergistic impacts emerged as common outcomes from co-infections, wherein both shifts and dispersion of microbial communities following co-infections were often more severe than after a single infection alone, but microbial α-diversity was not universally altered. Important functions of the microbiome may also suffer from such heavily altered, though no less species-rich microbial community. Lastly, we pose the hypothesis that the reshuffling of host-associated microbial communities due to the impact of various, often coinciding parasitic infections may become a source of novel or zoonotic diseases.