Species distribution models (SDMs) are an important class of model for mapping taxa spatially and are a key tool for tackling biodiversity loss. However, most common SDMs depend on presence–absence data and, despite the accumulation and exponential growth of biological occurrence data across the globe, the available data are predominantly presence-only (i.e. they lack real absences). Although presence-only SDMs do exist, they inevitably require assumptions about absences of the considered taxa and they are specified mostly for single species and, thus, do not exploit fully the information in related taxa. This greatly limits the utility of global biodiversity databases such as GBIF. Here, we present a Bayesian-based SDM for multiple species that operates directly on presence-only data by exploiting the joint distribution between the multiple ecological processes and, crucially, identifies the sampling effort per taxa which allows inference on absences. The model was applied to two case studies. One, focusing on taxonomically diverse taxa over central Mexico and another focusing on the monophyletic family Cactacea over continental Mexico. In both cases, the model was able to identify the ecological and sampling effort processes for each taxon using only the presence observations, environmental and anthropological data.