This study proposes a supercritical carbon dioxide Brayton cycle incorporating multi-stage main compressor intermediate cooling (MMCIC sCO2 Brayton cycle), and conducts an in-depth investigation and discussion on the enhancement of its thermodynamic performance. With the aim of achieving the maximum power cycle thermal efficiency and the maximum specific net work, this study examines the variation of the Pareto frontier with respect to the number of intermediate cooling stages and critical operational parameters. The results indicate that the MMCIC sCO2 Brayton cycle offers significant advantages in improving power cycle thermal efficiency, reducing energy consumption, and mitigating the adverse effects associated with main compressor inlet temperature increasing. Under the investigated operational conditions, the optimal cycle performance is achieved with four intermediate cooling stages, yielding a maximum power cycle thermal efficiency of 67.85% and a maximum specific net work of 0.177 MW·kg−1. Cycles with two or three intermediate cooling stages also deliver competitive cycle performance, and can be regarded as alternative options. Additionally, increasing the turbine inlet temperature proves more effective for enhancing power cycle thermal efficiency, whereas increasing the turbine inlet pressure can substantially improve the specific net work. This study provides a feasible structural layout approach and research framework to improve the thermodynamic performance of the sCO2 Brayton cycle, offering a robust theoretical foundation and technical guidance for its implementation in power engineering.