The non-specific binding of undesired ligands to a target is the primary factor limiting the enrichment of tight-binding ligands in affinity selection. Solution-phase non-specific affinity is determined by the free-energy of ligand binding to a single target. However, the solid-phase affinity might be higher if a ligand bound concurrently to multiple adjacent immobilized targets in a cooperative manner. Cooperativity could emerge in this case as a simple consequence of the relationship between the free energy of binding, localization entropy and the spatial distribution of the immobilized targets. We tested this hypothesis using a SELEX experimental design and found that non-specific RNA aptamer ligands can concurrently bind up to four bead-immobilized peptide targets, and that this can increase their effective binding affinity by two orders-of-magnitude. Binding curves were quantitatively explained by a new statistical mechanical model of density-dependent cooperative binding, which relates cooperative binding to both the target concentration and the target surface density on the immobilizing substrate. Target immobilization plays a key role in SELEX and other ligand enrichment methods, particularly in new multiplexed microfluidic purification devices, and these results have strong implications for optimizing their performance.