Dominating set in a mobile ad-hoc network (MANET) is a collection of devices acting as servers that store, forward, or backup data for other devices not in the set. To fulfill the service requirement, every device is either a dominator or adjacent to some dominator. Devices of the latter case are dominatees. To provide a more robust service, we can extend the definition of dominating set to k-dominating set, where each dominatee must be adjacent to at least k dominators (k is a constant). This paper proposes a self-stabilizing protocol that identifies a k-dominating set in a MANET. The identified set is guaranteed minimal in the sense that it contains no proper subset that is also a k-dominating set. We prove correctness and analyze stability property of this protocol. Simulation results indicate that the proposed protocol finds k-dominating sets of smaller size when compared with existing approaches.