Conventionally, non-orthogonal multiple access (NOMA) has traditionally been implemented separately from orthogonal multiple access (OMA), aiming to improve the capacity of multi-user systems. However, a recent study has ventured beyond this conventional approach by integrating OMA and NOMA proportionally within the same system. In spite of these advancements, the consideration towards optimizing multi-user systems remains incomplete especially when user service requirements vary significantly. Therefore, this paper explores a novel layered device-to-device (D2D) partial NOMA (P-NOMA) scheme, which introduces a hybrid power-domain access method into multi-user systems. The analysis primarily focuses on evaluating both the system performance and the impact of various parameters on it. In contrast to conventional fully overlapped NOMA signals, P-NOMA signals are partially overlapped with an overlap rate that can be determined based on quality-of-service (QoS) requirements. Simulation results demonstrate that judicious utilization of P-NOMA can effectively enhance overall system performance, particularly in terms of sum rate (SR) metrics, while also flexibly accommodating diverse QoS requirements for multiple users.