The increasing proliferation of Internet-of-things (IoT) networks in a given space requires exploring various communication solutions (e.g., cooperative relaying, non-orthogonal multiple access, spectrum sharing) jointly to increase the performance of coexisting IoT systems. However, the design complexity of such a system increases, especially under the constraints of performance targets. In this respect, this paper studies multiple-access enabled relaying by a lower-priority secondary system, which cooperatively relays the incoming information to the primary users and simultaneously transmits its own data. We consider that the direct link between the primary transmitter–receiver pair uses orthogonal multiple access in the first phase. In the second phase, a secondary transmitter adopts a relaying strategy to support the direct link while it uses non-orthogonal multiple access (NOMA) to serve the secondary receiver. As a relaying scheme, we propose a piece-wise and forward (PF) relay protocol, which, depending on the absolute value of the received primary signal, acts similar to decode-and-forward (DF) and amplify-and-forward (AF) schemes in high and low signal-to-noise ratio (SNR), respectively. By doing so, PF achieves the best of these two relaying protocols using the adaptive threshold according to the transmitter-relay channel condition. Under PF-NOMA, first, we find the achievable rate region for primary and secondary receivers, and then we formulate an optimization problem to derive the optimal PF-NOMA time and power fraction that maximize the secondary rate subject to reliability constraints on both the primary and the secondary links. Our simulation results and analysis show that the PF-NOMA outperforms DF-NOMA and AF-NOMA-based relaying techniques in terms of achievable rate regions and rate-guaranteed relay locations.