Solid-solid phase-change materials have great potential for developing compact and low-cost thermal storage systems. The solid-state nature of these materials enables the design of systems analogous to those based on natural rocks but with an extraordinarily higher energy density. In this scenario, the evaluation and improvement of the mechanical and thermophysical properties of these solid-solid PCMs are key to exploiting their full potential. In this study, LiNaSO4-based composites, comprising porous MgO and expanded graphite (EG) as the dispersed phases and LiNaSO4 as the matrix, have been prepared with the aim of enhancing the thermophysical and mechanical properties of LiNaSO4. The characteristic structure of MgO and the high degree of crystallinity of the EG600 confer on the LiNaSO4 sample mechanical stability, which leads to an increase in the Young’s modulus (almost three times higher) compared to the pure LiNaSO4 sample. These materials are proposed as a suitable candidate for thermal energy storage applications at high temperatures (400–550 °C). The addition of 5 wt.% of MgO or 5% of EG had a minor influence on the solid-solid phase change temperature and enthalpy; however, other thermal properties such as thermal conductivity or specific heat capacity were increased, extending the scope of PCMs use.