The fifth generation (5G) and beyond-5G networks aim to meet the rapidly growing traffic demands while considering the scarcity of radio resources and the heterogeneity of services and technical requirements. Non-Orthogonal Multiple Access (NOMA) has been considered a key technology to address resource scarcity by enabling more users to share the resources. Furthermore, network slicing tackles the requirements’ heterogeneity by partitioning the physical network into multiple logical slices. In this study, the aforementioned key technologies are adopted to maximize the overall throughput and satisfy the technical requirements of a multi-slice system. We formulate an optimization problem in a multi-slice cooperative NOMA-based system with underlay D2D communications that jointly addresses user grouping, radio resource blocks allocation, and D2D admission. Its objective is to maximize the overall system throughput while considering each slice’s constraints. Given the complexity of the optimization problem, we propose a three-step, low-complexity solution: a matching theory-based approach for the user grouping and the D2D admission sub-problems, and a heuristic approach for the resource blocks allocation sub-problem. [Numerical results demonstrate the: (1) low complexity of the proposed solution; (2) high impact of interference cancellation imperfection; (3) superior performance of the proposed solution compared to literature baselines. Specifically, under dense network, our solution achieves up to 34% enhancement in overall system throughput, up to 35% improvement in D2D admission, and up to 125% and 32%, respectively, in cellular users and D2D pairs satisfaction. It also outperforms under strict eMBB and URLLC requirements. Also, results show significant overestimation in Shannon’s evaluation of URLLC throughputs considered in some papers from the literature compared to the finite block length evaluation considered in our work, particularly at higher URLLC reliability requirements.