The aging population with its concomitant medical conditions, physical and cognitive impairments, at a time of strained resources, establishes the urgent need to explore advanced technologies that may enhance function and quality of life. Recently, robotic technology, especially socially assistive robotics has been investigated to address the physical, cognitive, and social needs of older adults. Most system to date have predominantly focused on one-on-one human robot interaction (HRI). In this paper, we present a multi-user engagement-based robotic coach system architecture (ROCARE). ROCARE is capable of administering both one-on-one and multi-user HRI, providing implicit and explicit channels of communication, and individualized activity management for long-term engagement. Two preliminary feasibility studies, a one-on-one interaction and a triadic interaction with two humans and a robot, were conducted and the results indicated potential usefulness and acceptance by older adults, with and without cognitive impairment.