Biomolecular condensates appear throughout the cell serving a wide variety of functions. Many condensates appear to form by the assembly of multivalent molecules, which produce phase-separated networks with liquidlike properties. These networks then recruit client molecules, with the total composition providing functionality. Here we use a model system of poly-SUMO and poly-SIM proteins to understand client-network interactions and find that the structure of the network plays a strong role in defining client recruitment and thus functionality. The basic unit of assembly in this system is a zipperlike filament composed of alternating poly-SUMO and poly-SIM molecules. These filaments have defects of unsatisfied bonds that allow for both the formation of a 3D network and the recruitment of clients. The filamentous structure constrains the scaffold stoichiometries and the distribution of client recruitment sites that the network can accommodate. This results in a nonmonotonic client binding response that can be tuned independently by the client valence and binding energy. These results show how the interactions within liquid states can be disordered yet still contain structural features that provide functionality to the condensate.