Verifying the compatibility of communicating peers is a crucial issue in critical distributed systems. Unlike the synchronous world, the asynchronous world covers a wide range of message ordering paradigms (e.g. FIFO or causal) that are instrumental to the compatibility of peer compositions. We propose a framework that takes into account the variety of asynchronous communication models and compatibility properties. The notions of peer, communication model, system and compatibility criteria are formalized in TLA+ to benefit from its verification tools. We present an implemented toolchain that generates TLA+ specifications from the behavioral descriptions of peers and checks compatibility of the composition with respect to given communication models and compatibility criteria.