Proteins interact with one another across a broad spectrum of affinities. Our understanding of the low end of this spectrum, as characterized by millimolar dissociation constants, relies on a handful of cases in which weak encounters have experimentally been identified. These weak interactions away from the specific target binding site can lead toward a higher-affinity complex. Recently, we detected weak encounters between two paralogous phosphotransferase pathways of Escherichia coli, which regulate various metabolic processes and stress responses. In addition to encounters that are known to occur between cognate proteins, i.e., those that can exchange phosphate groups with each other, surprisingly, encounters involving noncognates were also observed. It is not clear whether these "futile" encounters have a cooperative or competitive role. Using agent-based simulations, we find that the encounter complexes can be cooperative or competitive so as to increase or lower the effective binding affinity of the specific complex under different circumstances. This finding invites further questions into how organisms might exploit such low affinities to connect their signaling components.