Multi-agent systems draw together a number of significant trends in modern technology: ubiquity, decentralisation, openness, dynamism and uncertainty. As work in these fields develops, such systems face increasing challenges. Two particular challenges are decision making in uncertain and partially-observable environments, and coordination with other agents in such environments. Although uncertainty and coordination have been tackled as separate problems, formal models for an integrated approach are typically restricted to simple classes of problem and are not scalable to problems with tens of agents and millions of states. We improve on these approaches by extending a principled Bayesian model into more challenging domains, using Bayesian networks to visualise specific cases of the model and thus as an aid in deriving the update equations for the system. One approach which has been shown to scale well for networked offline problems uses finite state machines to model other agents. We used this insight to develop an approximate scalable algorithm applicable to our general model, in combination with adapting a number of existing approximation techniques, including state clustering. We examine the performance of this approximate algorithm on several cases of an urban rescue problem with respect to differing problem parameters. Specifically, we consider first scenarios where agents are aware of the complete situation, but are not certain about the behaviour of others; that is, our model with all elements but the actions observable. Secondly, we examine the more complex case where agents can see the actions of others, but cannot see the full state and thus are not sure about the beliefs of others. Finally, we look at the performance of the partially observable state model when the system is dynamic or open. We find that our best response algorithm consistently outperforms a handwritten strategy for the problem, more noticeably as the number of agents and the number of states involved in the problem increase.