In 2014, Rawlins and Wilson proposed a typology of agential interactions between users and designers of interactive data displays. This article tests that typology by studying 20 users working with three different types of interactive data displays and answering questions, which were coded by verb and actor and analyzed for themes. The authors show that rhetorical agency is marked by thoughts, actions, and language. Affordances by the designer open a shared rhetorical space where user and designer are coparticipants. As interactivity increases, participants see themselves as rhetorical agents in a community of rhetorical agents rather than as conduits of information.