The universality of the shape of the species–area relationship (SAR) is subject to regular debate. Recently, Storch et al. (2012) argued that species–area relationships collapse into a single curve at continental scales after the axes are rescaled adjusting the area-axis being to the mean range size of species and the species-axis to the species richness of an area equal to mean range size. It has been claimed that this rescaling generates a universal model, invariant of taxon and continent, and that it is driven by differences in range sizes. Here, we test the universality of the rescaled SAR across scales smaller than the continental level, using presence data for plants, birds and butterflies. We also test an alternative rescaling approach, by using the total extent of the study area and total species richness. At the scales analysed here, we found that the proposed rescaling by Storch et al. adjusts for differences in the extent of the study area and for variation in gamma diversity. Consequently, while the rescaled curves were closely aligned, they did not converge into a single curve. The observed remaining variation is independent of scale and biogeographical region, and is correlated with beta diversity; thus, it reflects the differentiation of species composition in space.