We present a cooperative, dual-stage (DS) non-orthogonal multiple access (NOMA) scheme for power line communication (PLC) systems, where three PLC modems are served in two time slots. The network consists of a source (S) modem, two relay (R) modems and a destination (D) modem. In each of the two time slots, S communicates with one R using NOMA, and the other R communicates with D using the decode-and-forward technique. We consider both scenarios where a direct link may or may not exist between S and D. We derive expressions for the approximate average sum rate and overall outage probability of the network. Next, we formulate an optimization problem to find the optimal power allocation coefficients at S, such that the sum rate is maximized. We establish the accuracy of our approximations using Monte Carlo simulations. Furthermore, we show that our scheme outperforms the two-user single-stage and the DS schemes, and the three-user NOMA scheme proposed in the earlier literature, in terms of sum rate and outage probability.INDEX TERMS Cooperative power line communication, dual-stage, non-orthogonal multiple access, outage probability, sum rate.