This paper proposes a power scaling (PS) technique aimed at mitigating the outage floor problem commonly encountered in multi-user full-duplex (FD) non-orthogonal multiple access (NOMA) systems. Two antenna modes denominated as adaptive antenna mode (AAM) and fixed antenna mode (FAM) are utilized in this work for L FD near users in close proximity. In addition, a combined method of selecting both antenna mode and near user integrated with PS is employed to improve the overall network performance. Moreover, a power allocation between the chosen near user and far user is considered. In the low-to-moderate power regions, by AAM and FAM, we achieve twice of full diversity gain and full diversity gain, respectively. The research presents mathematical expressions for deriving the average capacity and outage probability and supports the theoretical findings with simulation-based evidence. The results of this work show that PS method not only contributes to a greater spatial diversity but also leads to superior performance compared to traditional FD NOMA systems. Moreover, our proposed method overcomes the outage floor and capacity ceiling. Furthermore, the work can be developed to 6G massive MIMO technology in multi-user FD cooperative NOMA systems.