Prediction error is considered an important problem in species distribution models. To address this issue, we here examined the accuracy of overlays of presence-only-based models for many individual species in representing patterns of assemblage diversity. For this purpose, we used a database of 977 160 records of seed plant occurrences on an intensively surveyed, species-rich island (Tenerife, Canary Islands) for modelling the distribution of all its 841 native plant species individually. The modelling was done using Maxent, one of the best-performing presence-only modelling techniques, using various thresholds to convert the estimated suitability values into predicted presence or absence. Distribution models for each individual species were overlaid to predict species richness and composition, which were then compared to the observed values for well-surveyed grid cells. We found high levels of compositional error, when the best performing suitability threshold for predicting species richness was applied. Our best prediction had a mean species richness error of 24% and a mean compositional error of 60% relative to the observed values for the well-surveyed cells; >50% of all species were included erroneously in >25% of the well-surveyed cells. Hence, large quantities of data are not necessarily enough to obtain reliable predictions of assemblage diversity, limiting the usefulness of this methodology in conservation planning.