This paper offers a case study in undertaking a mutual shaping approach to the design of socially assistive robots. We consider the use of social robots in therapy, and we present our results regarding this application, but the approach is generalisable. Our methodology combines elements of user-centered and participatory design with a focus on mutual learning. We present it in full alongside a more general guide for application to other areas. This approach led to valuable results concerning mutual shaping effects and societal factors regarding the use of such robots early in the design process. We also measured a significant shift in participant robot acceptance pre-/post-study, demonstrating that our approach led to the two-way sharing and shaping of knowledge, ideas and acceptance.