To provide application-oriented network services, a variety of overlay networks are deployed over physical IP networks. Since they share and compete for the same physical network resources, their selfish behaviors affect each other and, as a result, their performance deteriorates. Our research group considers a model of overlay network symbiosis, where overlay networks coexist and cooperate to improve their application-level quality of service (QoS) while sustaining influences from the physical network and other overlay networks. In this paper, we especially focus on Peer-to-Peer (P2P) networks among various overlay networks. We propose a mechanism for pure P2P networks of file-sharing applications to cooperate with each other. In our proposal, cooperative peers establish logical links among two or more P2P networks, and messages and files are exchanged among cooperative P2P networks through these logical links. For efficient and effective cooperation, we also propose an algorithm for selection of cooperative peers and a caching mechanism to avoid putting too much load on cooperative peers and cooperating networks. Simulation results show that our proposed mechanism improves the search efficiency of P2P file-sharing applications and reduces the load in P2P networks.