Decentralized POMDPs are powerful theoretical models for coordinating agents’ decisions in uncertain environments, but the generally-intractable complexity of optimal joint policy construction presents a significant obstacle in applying Dec-POMDPs to problems where many agents face many policy choices. Here, we argue that when most agent choices are independent of other agents’ choices, much of this complexity can be avoided: instead of coordinating full policies, agents need only coordinate policy abstractions that explicitly convey the essential interaction influences. To this end, we develop a novel framework for influence-based policy abstraction for weakly-coupled transition-dependent Dec-POMDP problems that subsumes several existing approaches. In addition to formally characterizing the space of transition-dependent influences, we provide a method for computing optimal and approximately-optimal joint policies. We present an initial empirical analysis, over problems with commonly-studied flavors of transition-dependent influences, that demonstrates the potential computational benefits of influence-based abstraction over state-of-the-art optimal policy search methods.