Molten salts present significant advantages as coolants over traditional light water or gas. Salt-cooled nuclear reactor can potentially allow an increase in core power density and simplify the reactor safety case. Traditionally, molten salt reactors assume molten salt being both the fuel and the coolant. This, however, creates major challenges for the design and operation due to requirements for chemistry control and corrosion behaviour of the core structural materials. The Fluoride salt-cooled High-temperature Reactors (FHR) on the other hand, have conventional solid fuel geometry surrounded by moderator and coolant. Furthermore, some FHR variations share many common characteristics with the Advanced Gas-cooled Reactors (AGR). Thus, using the knowledge accumulated during many decades of successful AGR operation can speed up the FHR development and deployment. However, replacing carbon-dioxide coolant by molten salt significantly changes the reactor performance. Hence, a new core design is needed. In this work, a Multi-Objective Particle Swarm Optimisation is used to identify the most favourable configurations for a new system layout. Initially, the optimisation targeted the beginning of cycle parameters such as criticality and Coolant Temperature Coefficient (CTC). The present work is the next step in this analysis. Each configuration is examined with respect to its thermal-hydraulic performance to assess the power uprate potential which is limited by multiple temperature constraints (e.g. fuel centreline and cladding temperatures as well as the coolant freezing/boiling). The estimated maximum power was then used in the fuel burnup calculations, from which a discharge burnup and cycle average CTC were obtained. As a result of the optimisation process, several families of possible solutions were identified, which form an optimal Pareto front. The most attractive configurations in terms of achievable power density, however, were not necessarily on the Pareto front. Most of the identified design options had only a small amount of graphite moderator or no graphite at all, relying entirely on moderation in the salt. Increasing the graphite volume was consistently found to worsen most of the optimisation parameters. The newly identified design options have the potential to achieve power density which is higher than that of a typical AGR by up to a factor of five, while maintaining negative CTC through the burnup cycle.