This study examines a novel Solid Oxide Fuel Cell (SOFC) cogeneration system powered by liquefied natural gas integrating realistic and flexible heat management to support efficient maritime applications. With a nominal power capacity of 125 kW, the SOFC-based system comprises stacks and balance-of-plant components, including pre-reformer, afterburner, heat exchangers, and blowers. In addition to generating electricity for propulsion and onboard services, waste heat is recovered to produce saturated steam and hot water. Detailed process model was developed in Aspen Plus for both beginning (BoL) and end-of-life (EoL) conditions, followed by a multi-objective optimization targeting net electrical efficiency, external water intake, and external air flow. A suitable trade-off solution was selected for heat exchanger network (HEN) synthesis at EoL, and a mixed-integer linear programming model minimized the number of heat exchangers, determining optimal hot/cold stream matches under practical design constraints. These include forbidden matches, pressure drops, avoidance of high-temperature flow splitting/merging, and the creation of a hot box to reduce heat losses, enabling realistic, compact and marine-compatible layout. The resulting HEN was validated under BoL and part-load operation, confirming robustness and flexibility across the SOFC system's lifetime. The optimized system achieves 60.3% (BoL) and 50.2% (EoL) net electrical efficiency, producing 1788.3 kg/day of saturated steam and 1467.1 kg/day of hot water under EoL. A preliminary piping and instrumentation diagram was developed, incorporating safety and control loops, and valves and sensors. Overall, the study demonstrates the flexibility and robustness of SOFC-based cogeneration systems for efficient and practical maritime applications, advancing the integration of lower-emission technologies.