In supramolecular materials, multiple weak binding groups can act as a single collective unit when confined to a localized volume, thereby producing strong but dynamic bonds between material building blocks. This principle of multivalency provides a versatile means of controlling material assembly, as both the number and the type of supramolecular moieties become design handles to modulate the strength of intermolecular interactions. However, in materials with building blocks significantly larger than individual supramolecular moieties (e.g., polymer or nanoparticle scaffolds), the degree of multivalency is difficult to predict or control, as sufficiently large scaffolds inherently preclude separated supramolecular moieties from interacting. Because molecular models commonly used to examine supramolecular interactions are intrinsically unable to examine any trends or emergent behaviors that arise due to nanoscale scaffold geometry, our understanding of the thermodynamics of these massively multivalent systems remains limited. Here we address this challenge via the coassembly of polymer-grafted nanoparticles and multivalent polymers, systematically examining how multivalent scaffold size, shape, and spacing affect their collective thermodynamics. Investigating the interplay of polymer structure and supramolecular group stoichiometry reveals complicated but rationally describable trends that demonstrate how the supramolecular scaffold design can modulate the strength of multivalent interactions. This approach to self-assembled supramolecular materials thus allows for the manipulation of polymer-nanoparticle composites with controlled thermal stability, nanoparticle organization, and tailored meso- to microscopic structures. The sophisticated control of multivalent thermodynamics through precise modulation of the nanoscale scaffold geometry represents a significant advance in the ability to rationally design complex hierarchically structured materials via self-assembly.