Plant-soil feedbacks (PSFs) are considered a key mechanism generating frequency-dependent dynamics in plant communities. Negative feedbacks, in particular, are often invoked to explain coexistence and the maintenance of diversity in species-rich communities. A close connection between theoretical models and experimental approaches has enabled rapid progress in PSF research. However, the primary modeling framework used to study PSFs considers only two plant species, and we lack clear theoretical expectations for how these complex interactions play out in communities with natural levels of diversity. This discrepancy has attracted significant recent attention, because it is precisely in the most diverse communities that mechanisms of coexistence hold the greatest interest. To help bridge this gap, we generalize the classic theoretical model for PSFs to include any number of species and analyze the dynamics of this extended model. We demonstrate that this canonical model for PSFs is mathematically equivalent to a well-studied model from evolutionary game theory, and we use this equivalence to characterize the dynamics with an arbitrary number of plant species. Surprisingly, we find that robust coexistence of more than two species is virtually impossible. In particular, multispecies coexistence in this framework is neither dynamically nor structurally stable. Our results suggest that alternative theoretical frameworks are needed to describe feedbacks observed in diverse natural communities. Drawing on our analysis, we discuss general principles and future directions for PSF models, including several emerging alternative approaches. We also show how careful consideration of these theoretical foundations suggests important implications for experimental study of PSF-mediated coexistence in the field.