Several proposals on P2P-ISP cooperation have recently been developed using information sharing for locality-based peering. Their benefits in terms of P2P efficiency, ISP cost, and traffic localization have been demonstrated in the single ISP case. However, potential risks associated with such cooperation have not been well examined. This paper develops a taxonomy and a mathematical model to explore the unintended and counter-intuitive behaviors emerging out of these cooperations in the multiple ISP case. Through both numerical examples and analytical results, we illustrate how such behaviors may become damaging to both P2P providers and ISPs, and how they might be mitigated so that the full benefit of cooperation can be maintained.