Many robot-delivered health interventions aim to support people longitudinally at home to complement or replace in-clinic treatments. However, there is little guidance on how robots can support collaborative goal setting (CGS). CGS is the process in which a person works with a clinician to set and modify their goals for care; it can improve treatment adherence and efficacy. However, for home-deployed robots, clinicians will have limited availability to help set and modify goals over time, which necessitates that robots support CGS on their own. In this work, we explore how robots can facilitate CGS in the context of our robot CARMEN (Cognitively Assistive Robot for Motivation and Neurorehabilitation), which delivers neurorehabilitation to people with mild cognitive impairment (PwMCI). We co-designed robot behaviors for supporting CGS with clinical neuropsychologists and PwMCI, and prototyped them on CARMEN. We present feedback on how PwMCI envision these behaviors supporting goal progress and motivation during an intervention. We report insights on how to support this process with home-deployed robots and propose a framework to support HRI researchers interested in exploring this both in the context of cognitively assistive robots and beyond. This work supports designing and implementing CGS on robots, which will ultimately extend the efficacy of robot-delivered health interventions.