We consider a general multi-principal multi-agent contracting game in a complete-information 4supply-chain setting and determine coordinating equilibrium transfer schedules in closed form.The resulting contracts manage to align incentives for decentralized decision-making and achieve first-best channel solutions. We allow for multidimensional actions and arbitrary payoff externalities between all members of the supply chain. For the coordinating contracts to exist it suffices that all payoff functions are continuous on the compact action sets in a general sense that accommodates discrete action sets. Our approach unifies and generalizes a significant portion of the extant supply-chain literature. It can be applied to a very large class of many-to-many supply-chain settings.