Continuous hand rehabilitation at home is crucial in hemiplegic patients since there are many cases in which a patient leaves a hospital without sufficient recovery. Hand-rehabilitation-support robots have been proposed to support patients to continue rehabilitation at home. However, hemiplegic patients are quite different in their conditions of paralysis, especially in grip conditions. Therefore, due to their fixed hardware, most previous robots are usable only for specific patient conditions. Then, a patient should use many different robot types during recovery. To overcome this problem, we propose a new configurable robot that rehabilitates patients with various paralytic hand conditions with a single robot. The robot's assist mechanisms are easily replaceable so that it adopts a wide range of grip conditions unique to each hemiplegic hand. This paper shows the mechanism and the experimental results showing that the robot produces sufficient assist forces against various gripping forces.