This paper develops a multiperiod multiobjective optimization procedure to determine the optimal configuration and operational strategy of a trigeneration system assisted with solar-based technologies and thermal energy storage. The optimization model, formulated as mixed integer linear programming problem, incorporates dynamic operating conditions through time-dependent local climatic data, energy resources, energy demands, electricity prices, and electricity CO2 emission factors. The methodology is applied to a case study of a residential building in Spain. First, the single-objective solutions are obtained, highlighting their fundamental differences regarding the installation of cogeneration (included in the optimal total annual cost solution) and solar-based technologies (included in the optimal total annual CO2 emissions solution). Then, the Pareto curve is generated, and a decision-making approach is proposed to select the preferred trade-off solutions based on the marginal cost of CO2 emissions saved. Additionally, sensitivity analyses are performed to investigate the influence of key parameters concerning energy resources prices, investment costs, and rooftop area. The analyses of the trade-off solutions verify the enormous potential for CO2 emissions reduction, which can reach 32.3% with only 1.1% higher costs by displacing cogeneration in favor of the heat pump and the electric grid. Besides, with a modest cost increase of 7.3%, photovoltaic panels are incorporated, promoting an even greater CO2 emissions reduction of 45.2%.