This paper presents a theoretical investigation of a new configuration of the combined power and cooling cycle known as the Goswami cycle. The new configuration consists of two turbines operating at two different working pressures with a low-heat source temperature, below 150 °C. A comprehensive analysis was conducted to determine the effect of key operation parameters such as ammonia mass fraction at the absorber outlet and boiler-rectifier, on the power output, cooling capacity, effective first efficiency, and effective exergy efficiency, while the performance of the dual-pressure configuration was compared with the original single pressure cycle. In addition, a Pareto optimization with a genetic algorithm was conducted to obtain the best power and cooling output combinations to maximize effective first law efficiency. Results showed that the new dual-pressure configuration generated more power than the single pressure cycle, by producing up to 327.8 kW, while the single pressure cycle produced up to 110.8 kW at a 150 °C boiler temperature. However, the results also showed that it reduced the cooling output as there was less mass flow rate in the refrigeration unit. Optimization results showed that optimum effective first law efficiency ranged between 9.1% and 13.7%. The maximum effective first law efficiency at the lowest net power (32 kW) and cooling (0.38 kW) outputs was also shown. On the other hand, it presented 13.6% effective first law efficiency when the net power output was 100 kW and the cooling capacity was 0.38 kW.