A programmable ligand display system can be used to dissect the multivalent effects of ligand binding to a membrane receptor. An antagonist of the A2A adenosine receptor, a G-protein-coupled receptor that is a drug target for neurodegenerative conditions, was displayed in 35 different multivalent configurations, and binding to A2A was determined. A theoretical model based on statistical mechanics was developed to interpret the binding data, suggesting the importance of receptor dimers. Using this model, extended multivalent arrangements of ligands were constructed with progressive improvements in binding to A2A. The results highlight the ability to use a highly controllable multivalent approach to determine optimal ligand valency and spacing that can be subsequently optimized for binding to a membrane receptor. Models explaining the multivalent binding data are also presented.