With increasing demand in rich content driving up the need for increased system capacity, novel transmission techniques are required for future mobile networks. In this paper, a novel cache-aided (CA) device-to-device (D2D) non-orthogonal multiple access (NOMA) system employing cache-enabled interference cancellation (CIC) is proposed to increase the system sum rate performance. Utilising the uplink channels of a pair of users, the proposed system allows both users to exchange previously cached content with each other over a D2D link instead of receiving them only from the base station in conventional approaches. The sum rate of the proposed approach is derived and analysis shows an exact region in which it outperforms CANOMA. Simulation results verify the analytical results that when the users are close together, CA-D2D NOMA is the preferred choice of transmission technique over CA-NOMA. The results also show that the best sum rate performance is obtained when the system switches between the two NOMA schemes based on the derived regions.