The Dorsal Grasper, an assistive wearable grasping device, incorporates supernumerary fingers and an artificial palm with the forearm and back of the hand, respectively. It enables power wrap grasping and adduction pinching with its V-shaped soft fingers. Designed with C6/C7 spinal cord injury in mind, it takes advantage of active wrist extension that remains in this population after injury. We propose that allowing the operator to actively participate in applying grasp forces on the object, using the back of the hand, enables intuitive, fast and reliable grasping relevant for the execution of activities of daily living. Functional grasping is tested in three normative subjects and a person with C6 SCI using the Grasp and Release Test. Results indicate that this device provides promising performance on a subset of objects that complements the existing compensatory strategies used by people with C6/C7 SCI. We find that the addition of the artificial palm is important for increasing maximum grip strength, by increasing contact friction and protecting the opisthenar.