The appropriate sensory information feedback is important for the success of an object grasping and manipulation task. In many scenarios, the need arises for multiple feedback information to be conveyed to a prosthetic hand user simultaneously. The multiple sets of information may either (1) directly contribute to the performance of the grasping or object manipulation task, such as the feedback of the grasping force, or (2) simply form additional independent set(s) of information. In this paper, the efficacy of simultaneously conveying two independent sets of sensor information (the grasp force and a secondary set of information) through a single channel of feedback stimulation (vibrotactile via bone conduction) to the human user in a prosthetic application is investigated. The performance of the grasping task is not dependent to the second set of information in this study. Subject performance in two tasks: regulating the grasp force and identifying the secondary information, were evaluated when provided with either one corresponding information or both sets of feedback information. Visual feedback is involved in the training stage. The proposed approach is validated on human-subject experiments using a vibrotactile transducer worn on the elbow bony landmark (to realize a non-invasive bone conduction interface) carried out in a virtual reality environment to perform a closed-loop object grasping task. The experimental results show that the performance of the human subjects on either task, whilst perceiving two sets of sensory information, is not inferior to that when receiving only one set of corresponding sensory information, demonstrating the potential of conveying a second set of information through a bone conduction interface in an upper limb prosthetic task.