Multiplexity, the pattern that individuals interact on not only one, but multiple types of relationships, is an important but largely understudied topic. Consider an individual who has an additional link, with whom will she form the link? With a current neighbor (i.e., to multiplex), or a stranger? Under which conditions will the individual prefer one over another? We build a theoretical model to study this problem. Individu- als cooperate with their neighbors on networks. We find the following: 1) Multiplexity enhances cooperation because various relationships serve as social collateral for each other. 2) Individuals can fall into a “multiplexity trap” ? due to the high benefits of multiplexity in sustaining cooperation, agents may keep adding relationships with cur- rent neighbor(s), even if it is more efficient to cooperate with a stranger. 3) Individuals tend to multiplex if the current network has a less dispersed degree distribution (i.e., all individuals have similar numbers of friends), or exhibits a homophily in terms of degrees (i.e., more connected agents tend to link with each other). We also provide empirical analysis using the Indian Village Survey Data provided by Jackson et al. (2012) and Banerjee et al. (2013), which document networks with seven different types of relationships in each of the 77 rural villages. Our empirical analysis shows strong evidence of multiplexity, and is consistent with our theoretical predictions.