In this study, the production of power, heating, cooling, freshwater, hydrogen and ammonia in a gas turbine cycle (GTC)-based multi-energy system is analysed. From parametric study with energy, exergy, economic, environmental and exergo-enviro analyses, regression models were created for five different responses depending on the decision parameters. These are exergy efficiency (flex), dynamic payback period (DPP-year), CO2 footprint (kg/kWh), net present value (NPV-$) and levelized multi energy cost (LMEC-$/GJ). With these response values, bi-objective (BO), tri-objective (TO) and multi-objective optimization (MOO) studies including all responses were performed with Response Surface Method (RSM) and desirability function approach under various scenarios. In this context, RSM desirability plots and scores were generated by analyzing all binary (C(5,2)) and ternary C (5,3)) combinations of five different responses and MOO. As a result, a high desirability score of 0.8584 was obtained in MOO and an improvement of 2.19, 22.44, 1.37, 11.41 and 8.82 % was achieved for flex, DPP-year, CO2 footprint-kg/kWh, NPV-$, and LMEC-$/GJ, respectively compared to the base case. Based on all response values pertaining to the energy, exergy, economic, environmental performance of the multi-energy system with RSM optimization, a performance enhancement of 9.25 % was determined.