Socially assistive robots are increasingly being designed to interact with humans in various therapeutical scenarios. We believe that one useful scenario is providing exercise coaching for Persons with Dementia (PWD), which involves unique challenges related to memory and communication. We present a design for a robot that can seek to help a PWD to conduct exercises by recognizing behaviors and providing feedback, in an online, multimodal, and engaging way. Additionally, in line with a mid-fidelity prototyping approach, we report on some feedback from an exploratory user study using a Baxter robot, which provided some confirmation of the usefulness of the general scenario; furthermore, the results suggested the degree of a robot's feedback could be tailored to provide impressions of attentiveness or fun. Limitations and possibilities for future improvement are outlined, touching on deep learning and haptic feedback, toward informing next designs.