Herein, a novel three-stage cascade power/cooling cogeneration system that includes the gas turbine (GT) cycle, supercritical CO2 Brayton cycle (S-CO2), transcritical CO2 Rankine cycle (T-CO2), and organic Rankine cycle is proposed. The system is simulated by connecting MATLAB and Aspen HYSYS via Active-X control. It is indicated in the results that the system exhibits power generation, primary energy utilization, and exergy efficiencies of 59.43%, 81.66%, and 53.94%, respectively. The total product cost and environmental cost per unit exergy are 23.80 and 32.66 $GJ(-1), respectively. Monoethanolamine is used to absorb CO2 from the exhaust gas, and cold energy from liquefied natural gas is utilized to capture carbon, with a capture rate of 96%, to realize low-carbon-emission characteristics. Additionally, the performance of the established system is verified using three basic cycles for comparison. It is revealed in the results that the designed system exhibits the highest thermodynamic performance and net present value among the investigated cycles. Furthermore, multi-objective optimization of the systems is performed using the second-generation non-dominated sorting genetic algorithm algorithm. Although the GT/S-CO2/T-CO2 cycle is found to be more cost-effective than the proposed system at generation efficiencies less than 55%, the established system is deemed the best option among the cycles at power-generation efficiencies greater than 55%.