The design of solid oxide fuel cells (SOFC) using biogas for distributed power generation is a promising alternative to reduce greenhouse gas emissions in the energy and waste management sectors. Furthermore, the high energy conversion efficiency of SOFCs in conjunction with the possibilities to co-generate hydrogen may provide the economic viability that conventional fuel cell systems lack. However, the influence of operational parameters as design variables in the optimization of revenues and efficiency has been seldom studied for these novel cogeneration systems. Thus, in order to fulfill this knowledge gap, a multi-objective optimization problem using the NSGA-II algorithm is proposed to evaluate optimal solutions for cogeneration systems producing hydrogen and electricity from biogas. Furthermore, a mixed-integer linear optimization routine is used to ensure an efficient heat recovery system with minimal number of heat exchanger units. The results indicate that SOFC systems with hydrogen production are able to achieve higher efficiencies (5-17%) and a drastic improvement in net present value (140-170%). Despite the additional equipment to hydrogen enrichment and purification, the investment costs are estimated to be quite similar (5% difference) for optimal NPV solutions. The differences between the proposed scenarios (hydrogen cogeneration vs sole power conversion) and the effect of the design variables are investigated and discussed. In view of the advantages of hydrogen cogeneration, with financial incentives and the establishment of a hydrogen market, the transition of biogas plants to polygeneration systems is foreseen.