Buildings exert substantial influence on worldwide energy consumption, carbon emissions, and the depletion of freshwater resources. The endeavor to formulate ecologically conscious and energy-efficient building designs constitutes a multifaceted optimization, owing to the intricate interdependencies within the building energy-carbon-water nexus. This paper proposes an innovative multi-phase and multi-objective genetic framework that combines Energy Plus with databases containing embodied energy, embodied carbon, and embodied water data. This integrated approach enables the holistic assessment and optimization of operational and embodied energy and resulting carbon emissions and embodied water footprint under weather condition. By manipulating design variables such as geometrical and envelope-related parameters, the framework identifies the optimal building configuration. This methodology is applied to an office building model located in Dulles, Virgina, achieving optimization across three phases for present weather data: operational energy-embodied energy trade-off, operational carbon-embodied carbon trade-off, and total carbon and embodied water reduction. The results show a conflict between total carbon emissions and embodied water consumption. In the initial optimization stage, total operational energy decreases by 6.8 %, whereas its embodied energy by 1.8%, compared to the original design. In the second phase, there are reductions of 8% and 12.2% in operational and embodied carbon footprint, respectively. The third optimization phase leads to an 8.7 % reduction in total carbon emissions and 43.7% increase in embodied water.