Improved solute selectivity, an issue commonly approached through the development of advanced membrane materials, can be achieved through staged diafiltration processes. A mathematical model that describes the solute concentration profile within a single diafiltration module is developed and experimentally validated. For this module, where the diafiltrate is introduced uniformly over its length, a critical diafiltrate flux that results in the retentate concentration remaining constant during operations is identified. The model is then extended to examine two configurations of multistage diafiltration cascades: stripping sections and rectifying sections. The two configurations differ based on the connectivity between stages. Namely, stripping sections connect multiple modules by utilizing the retentate from one stage as the feed to the subsequent stage while the permeate is repurposed as the diafiltrate. In contrast, rectifying sections utilize the permeate from one stage as the feed to the subsequent stage and the retentate becomes the diafiltrate. For cascades that operate with a constant diafiltrate to feed flow ratio for all stages, the analysis demonstrates that stripping sections can reduce the diafiltrate consumed when separating low molar mass impurities from larger, impermeable molecules. On the other hand, cascades in a rectifying section configuration can improve the separation of two solutes with finite sieving coefficients between 0 and 1. Finally, asymmetric cascades, i.e., systems in which each stage has a unique diafiltrate to feed flow ratio, are shown to be capable of improving the recovery and purity of solutes in effluent streams relative to systems that operate at constant a diafiltrate to feed ratio. As a whole, the study highlights that the continued advancement of membrane separations will rely equally on thoughtful module and process design as well as the development of new materials.