It is useful to provide composers on mobile computers that dynamically compose the services offered by a set of networked devices. For example, a mobile computer could execute a multi-device composer that provides an operation for simultaneously turning off a set of lights rather than through their individual user-interfaces (UIs). This paper addresses the issue of flexibly and generically supporting multi-device composition. It makes the following novel contributions: (a) an identification of composition semantics that apply to a wide variety of devices, (b) a classification and evaluation of several existing mechanisms for supporting these semantics, and (c) an evaluation of a new composition framework that combines and extends existing, seemingly unrelated, approaches. The key to integrating these approaches is basing composition on programming patterns, which provide a bridge between the operation oriented and data oriented approaches. Our framework uses the existing ideas of allowing a single composer to work for a family of device classes and providing some composers that are based on UI generation. It extends these ideas by allowing a composer to be based on the programming patterns used in the device classes rather than the interfaces they implement to support all identified composition semantics.