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 their behaviors and providing appropriate feedback, in an online, multimodal, and engaging way. Additionally, following a mid-fidelity prototyping approach, we report on some observations from an exploratory user study using a Baxter robot; although limited by the sample size and our simplified approach, the results suggested the usefulness of the general scenario, and that the degree to which a robot provides feedback–occasional or continuous– could moderate impressions of attentiveness or fun. Some possibilities for future improvement are outlined, touching on richer recognition and behavior generation strategies based on deep learning and haptic feedback, toward informing next designs. © 2020 IEEE.