In light of the environmental and economic barriers of biomass-driven hybrid systems, this study investigates an integrated multi-generation biomass-powered system for electricity, freshwater, and cooling production. The proposed configuration combines a modified Brayton cycle (BC), reverse osmosis (RO) desalination unit, steam Rankine cycle (SRC), absorption chiller, and thermoelectric generator (TEG), which recovers waste heat from biomass combustion to enhance overall efficiency. System interactions are modeled through an exergoeconomic approach developed in EES software and validated against literature benchmarks. A bi-level multi-objective optimization framework, combining a statistical optimization model with a genetic algorithm (GA), is applied to maximize exergy efficiency while simultaneously minimizing the cost rate and CO2 emissions. The system's dynamic performance is evaluated across three case studies selected based on biomass availability, cooling demand, and desalination requirements. The findings demonstrate that the proposed optimization framework effectively manages the trade-offs among conflicting design objectives, achieving a peak exergy efficiency of 21.23 %, a minimized cost rate of 22.28 $/h, and CO2 emissions of 0.902 kg/h. The exergoeconomic analysis highlights an overall exergy destruction rate of 1,180 kWh, with the modified BC and the SRC identified as the most cost-intensive subsystems, contributing 17.75 $/h and 2.24 $/h, respectively. In contrast, the RO desalination unit exhibits the lowest cost contribution at 0.25 $/h. Dynamic simulations further indicate that the system can generate up to 53.457 MWh/year of renewable electricity, leading to an annual CO2 emissions reduction of 10,905 tons. Under optimal operating conditions, the semi-arid climate scenario (Iran) achieves a peak freshwater production rate of 16.2 m3/h in December, whereas the humid subtropical climate scenario (Australia) delivers the highest cooling output of 46.1 kWh in June.