Increasingly, systems are composed from independently developed parts, and mechanisms that allow those parts to interact (connectors). In many situations, specialized forms of interaction are needed to bridge component mismatches or to achieve extra-functional properties (e.g., security, performance, reliability), making the design and implementation of these interaction mechanisms a critical issue. Unfortunately, system developers have few options: they must live with available, but often inadequate, generic support for interaction (such as RPC), or they must handcraft specialized mechanisms at great cost. In this paper we describe a partial solution to this problem, whereby interaction mechanisms are constructed compositionally. Specifically, we describe a set of operators that can transform generic communication mechanisms (such as RPC and publish-subscribe) to incrementally add new capabilities. We show how these transformations can be used to realize complex interactions (such as Kerberized RPC) and to generate implementations of the new connector types at relatively low cost.