In many situations, cell-cell adhesion is mediated by multiple ligand-receptor pairs. For example, the interaction between T cells and antigen-presenting cells of the immune system is mediated not only by T cell receptors and their ligands (peptide-major histocompatibility complex) but also by binding of intracellular adhesion molecules. Interestingly, these binding pairs have different resting lengths. Fluorescent labeling reveals segregation of the longer adhesion molecules from the shorter T cell receptors in this case. Here, we explore the thermal equilibrium of a general cell-cell interaction mediated by two ligand-receptor pairs to examine competition between the elasticity of the cell wall, nonspecific intercellular repulsion, and bond formation, leading to segregation of bonds of different lengths at equilibrium. We make detailed predictions concerning the relationship between physical properties of the membrane and ligand-receptor pairs and equilibrium pattern formation, and suggest experiments to refine our understanding of the system. We demonstrate our model by application to the T cell/antigen-presenting-cell system and outline applications to natural killer cell adhesion.