Most organisms are built from a single genome. In striking contrast, arbuscular mycorrhizal fungi appear to maintain genomic variation within an individual fungal network. Arbuscular mycorrhizal fungi dwell in the soil, form mutualistic networks with plants, and bear multiple, potentially genetically diverse nuclei within a network. We explore, from a theoretical perspective, why such genetic diversity might be maintained within individuals. We consider selection acting within and between individual fungal networks. We show that genetic diversity could provide a benefit at the level of the individual, by improving growth in variable environments, and that this can stabilize genetic diversity even in the presence of nuclear conflict. Arbuscular mycorrhizal fungi complicate our understanding of organismality, but our findings offer a way of understanding such biological anomalies.