Enhancing efficiency, meeting environmental standards, and preserving fuel resources are highly important objectives in power generation systems, at a time where world is endangered by several energetic, environmental, and health crises. Thus, better designs are constantly sought to increase the performance of such systems. In this study, an environment friendly trigeneration system based on solid oxide fuel cell (SOFC) is selected and designed for domestic applications. Negligible emissions are thus recorded as the SOFC is fueled solely by hydrogen. The system is modeled following three steps: the energy simulation of residential building to determine its demands, the system’s prime mover–SOFC, and the trigeneration recovery system ensuring the maximum coverage of heating, cooling, and domestic hot water loads respectively. The system is then evaluated under the 4-E assessment criteria: energy, exergy, economy, and environment. Depending on these criteria, the system is multi-objectively optimized. Two operation strategies are adopted: off-grid following electrical load and on-grid base load operations. Optimization results show that the trigeneration system is energetically and economically superior and performs well under both strategies. The maximum energy and exergy efficiencies (65.2% and 45.77%) and minimum system cost rate (22.2 cents/kWh) are obtained under on-grid base load operation.