Species occurrence is influenced by environmental conditions and the presence of other species. Current approaches for multispecies occupancy modelling are practically limited to two interacting species and often require the assumption of asymmetric interactions. We propose a multispecies occupancy model that can accommodate two or more interacting species. We generalize the single-species occupancy model to two or more interacting species by assuming the latent occupancy state is a multivariate Bernoulli random variable. We propose modelling the probability of each potential latent occupancy state with both a multinomial logit and a multinomial probit model and present details of a Gibbs sampler for the latter. As an example, we model co-occurrence probabilities of bobcat (Lynx rufus), coyote (Canis latrans), grey fox (Urocyon cinereoargenteus) and red fox (Vulpes vulpes) as a function of human disturbance variables throughout 6 Mid-Atlantic states in the eastern United States. We found evidence for pairwise interactions among most species, and the probability of some pairs of species occupying the same site varied along environmental gradients; for example, occupancy probabilities of coyote and grey fox were independent at sites with little human disturbance, but these two species were more likely to occur together at sites with high human disturbance. Ecological communities are composed of multiple interacting species. Our proposed method improves our ability to draw inference from such communities by permitting modelling of detection/non-detection data from an arbitrary number of species, without assuming asymmetric interactions. Additionally, our proposed method permits modelling the probability two or more species occur together as a function of environmental variables. These advancements represent an important improvement in our ability to draw community-level inference from multiple interacting species that are subject to imperfect detection.