Bifunctional coupling of two different catalytic site types has often been invoked to explain experimentally observed enhanced catalytic activities. We scrutinize such claims with generic scaling-relation-based microkinetic models that allow exploration of the theoretical limits for such a bifunctional gain for several model reactions. For sites at transition-metal surfaces, the universality of the scaling relations between adsorption energies largely prevents any improvements through bifunctionality. Only the consideration of systems that involve the combination of different materials, such as metal particles on oxide supports, offers hope for significant bifunctional gains. The gains in catalytic activity that are achievable through bifunctional coupling by diffusion (between two sites s and t; see picture) are assessed using generic reaction schemes and a descriptor-based approach. The analysis predicts that only the coupling of different classes of materials, such as metals and oxides, can give rise to substantial gains.