The paradigm of the Internet of Things predicts that not only typical computing devices but also mundane objects will soon cooperate to achieve certain goals and communicate with users. In this paper we present a new way of designing multi-device interaction to accommodate diverse types of devices and relations among them. We first held a design workshop wherein participants created new multi-device interaction ideas by using device cards. We then analyzed the ideas in terms of the roles of devices, relations of devices with the user/environment, data type and data flow direction. Based on the findings, we identified 10 device roles and developed the corresponding diagram building blocks, each of which clearly visualizes its interaction partner and data flow characteristics. Our own investigation and additional design workshop showed that the building blocks along with device cards can help quickly create and improve multi-device interaction ideas with completeness.