Hybrid solar power plants which combine concentrated solar power (CSP) and photovoltaic (PV) systems with thermal energy storage (TES) have the potential to provide cost competitive and dispatchable renewable energy. The integration of energy storage gives dispatchability to the variable renewable generation while the combination of different generation technologies can reduce the costs. However, the design of reliable and cost competitive hybrid solar power plants requires the careful balancing of trade-offs between financial and technical performance. This is made more complicated by the dependence on a larger number of parameters compared to conventional plants and due to the integration of TES which requires that the operational profile is optimised for every design. This contribution presents a two-stage, multi-objective optimisation framework which combines multi-objective linear programming methods for the operational optimisation with multi-objective genetic algorithms for the design optimisation. The operational optimisation which is performed for every design point needs to be performed with linear programming methods. Here an automated scalarisation method is developed for the linear programming method which enables the multi-objective optimisation of the operational profile. This enables the evaluation of the trade-offs between financial and technical performance in both the design and operational optimisation, which is required to design reliable and cost competitive sustainable energy systems. The two-stage multi-objective optimisation is applied to analyse and improve the design of the hybrid solar power plant Atacama-1. It is demonstrated that balancing the trade-off between financial and technical performance is key to increase the competitiveness of solar energy and that it is possible to simultaneously increase dispatchability and decrease the levelised cost of energy. This shows that the operational and design optimisations have to be directly linked in order to exploit the synergies of hybrid systems. Thus the optimisation framework presented in this study can improve the decision making in the design of hybrid solar power plants.