Rehabilitation training for patients with motor disabilities usually requires specialized devices in rehabilitation centers. Home-based multi-purpose training would significantly increase treatment accessibility and reduce medical costs. While it is unlikely to equip a set of rehabilitation robots at home, we investigate the feasibility to use the general-purpose collaborative robot for rehabilitation therapies. In this work, we developed a new system for multi-purpose upper-limb rehabilitation training using a generic robot arm with human motor feedback and preference. We integrated surface electromyography, force/torque sensors, RGB-D cameras, and robot controllers with the Robot Operating System to enable sensing, communication, and control of the system. Imitation learning methods were adopted to imitate expert-provided training trajectories which could adapt to subject capabilities to facilitate in-home training. Our rehabilitation system is able to perform gross motor function and fine motor skill training with a gripper-based end-effector. We simulated system control in Gazebo and training effects (muscle activation level) in OpenSim and evaluated its real performance with human subjects. For all the subjects enrolled, our system achieved better training outcomes compared to specialist-assisted rehabilitation under the same conditions. Our work demonstrates the potential of utilizing collaborative robots for in-home motor rehabilitation training.