Solid oxide fuel cells (SOFCs) offer broad fuel flexibility and high overall energy-conversion efficiency. They are commonly integrated with gas turbines (GTs) or micro gas turbines (MGTs) to recover exhaust heat. However, incomplete heat recovery and poor thermal matching in bottoming cycles remain unresolved. To enable efficient cascade utilization of medium- and high-temperature flue-gas heat, this study proposed an SOFC-MGT-SRCO2-DPORC integrated power generation system. The system combines an SOFC-MGT topping cycle with a recuperative supercritical carbon dioxide cycle (SRCO2) and a dual-pressure organic Rankine cycle (DPORC). A thermodynamic model incorporating SOFC electrochemical behavior was established. The effects of operating parameters on thermodynamic performance were evaluated, followed by parameter optimization and comparisons under optimal conditions. The proposed system achieved the best overall performance among the investigated configurations. Its net power output and thermal efficiency reached 4.158 kW and 77.489%, respectively. Its exergy efficiency was 4.73% higher than that of the SOFC–MGT–SRCO2 system on a relative basis. These results provide a theoretical basis for improving the performance of integrated SOFC power systems.