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Peer-to-Peer (P2P) Video-on-Demand (VoD) systems with multiple channels are called multi-channel P2P VoD systems, which can be categorized into independent-channel P2P VoD systems and correlated-channel P2P VoD systems. Most of the existing P2P VoD systems are independent-channel P2P systems, in which the peers share resources with each other within the same channel. In this paper, we examine the cross-channel resource sharing in correlated-channel P2P VoD systems. We optimize the server upload allocations among channels to maximize the average streaming capacity. Furthermore, we introduce bandwidth amplifiers to establish cross-channel links, thus enabling cross-channel sharing of peer upload bandwidths. We demonstrate in the simulations that the correlated-channel P2P VoD systems with cross-channel resource sharing can achieve a higher average streaming capacity compared to the independent-channel P2P VoD systems without cross-channel resource sharing.