In recent years, wireless communication has experienced a massive shift from a single service (i.e., voice) to an interconnected web of networks. Although many techniques have been developed improving the offered services to mobile users, still the demand for high-quality services cannot be reached. Therefore, this paper proposes a joint non-orthogonal multiple access (NOMA)-enabled optimization framework for small-cell network (SCNet) by utilizing the concepts of multi-objective problem. In particular, the transmit power of base station (BS) in each small-cell simultaneously optimizes to maximize the sum-capacity and total energy efficiency (EE) of SCNet. The multi-objective optimization problem is formulated as non-convex subject to several practical constraints, i.e., individual quality of service requirement, maximum power budget of small-cell BS, and efficient decoding of superimposed signal using successive interference cancellation. Based on the nature of the problem, the optimal solutions are provided using sequential quadratic programming, and Karush-Kuhn-Tucker approaches. The obtained results show significant performance gains over conventional orthogonal multiple access technique in terms of sum-capacity and total EE.