The species abundance distribution (SAD) is one of the few universal patterns in ecology. Research on this fundamental distribution has primarily focused on the study of numerical counts, irrespective of the traits of individuals. Here we show that considering a set of Generalized Species Abundance Distributions (GSADs) encompassing several abundance measures, such as numerical abundance, biomass and resource use, can provide novel insights into the structure of ecological communities and the forces that organize them. We use a taxonomically diverse combination of macroecological data sets to investigate the similarities and differences between GSADs. We then use probability theory to explore, under parsimonious assumptions, theoretical linkages among them. Our study suggests that examining different GSADs simultaneously in natural systems may help with assessing determinants of community structure. Broadening SADs to encompass multiple abundance measures opens novel perspectives in biodiversity research and warrants future empirical and theoretical developments.