Solid oxide fuel cells (SOFC) have developed to a mature technology, able to achieve electrical efficiencies beyond 60%. This makes them particularly suitable for off-grid applications, where SOFCs can supply both electricity and heat at high efficiency. Concerns related to lifetime, particularly when operated dynamically, and the high investment cost are however still the main obstacles toward a widespread adoption of this technology. In this paper, we propose a hybrid cogeneration system that attempts to overcome these limitations, in which the SOFC mainly provides the baseload of the system. Introducing a purification unit allows the production and storage of pure hydrogen from the SOFC anode off-gas. The hydrogen can be stored, and used in a proton exchange membrane fuel cell (PEMFC) during peak demands. The SOFC system is completed with a battery, used during periods of high electricity production. We propose the use of a mixed integer-linear optimization framework for the sizing of the different components of the system, and particularly for identifying the optimal trade-off between round-trip efficiency and investment cost of the battery-based and hydrogen-based storage systems. The proposed system is applied and optimized to two case studies: an off-grid dwelling, and a cruise ship. The results show that, if the SOFC is used as the main energy conversion technology of the system, the use of hydrogen storage in combination with a PEMFC and a battery is more economically convenient compared to the use of the SOFC in stand-alone mode, or of pure battery storage. The results show that the proposed hybrid storage solution makes it possible to reduce the investment cost of the system, while maintaining the use of the SOFC as the main energy source of the system.