Peer-to-Peer(P2P) streaming has become a very popular technique to realize live media broadcast over the Internet. Most previous research of P2P streaming focuses on the delivery of a single media stream (called a channel). The widely deployed implementations, however, all concurrently offer multiple channels through their P2P networks. This paper investigates the overlay organization for multi-channel P2P streaming systems through modeling and simulations. In particular, this paper examines the potential collaborations among nodes across multiple channels. Our investigation shows that collaboration among nodes across different channels can improve the overall performance of the multi-channel P2P streaming system. However, the collaboration strategies need to be carefully selected. Simple collaboration strategies, such as treating collaborative nodes (those "borrowed" from other channels) the same as a channel's native nodes (those playing the channel), tend to have marginal or even negative effects on the whole system performance. This result is contrary to common impression - the larger population the better performance of P2P system - and we found that this is caused by the differences between P2P streaming and traditional P2P file-sharing systems. Furthermore, this paper proposes a set of simple strategies that controls the upload-download ratio of collaborative nodes. We showed that this set of strategies produces a much better collaboration result for multi-channel P2P streaming systems. Although only a preliminary study, we believe the results will promote further investigation on the topic of multi-channel P2P streaming.