Solar thermal power technologies require storage systems to mitigate the natural variability of solar irradiation. Packed bed thermal storage systems (PBTES) offer a cost-effective solution using air as heat transfer fluid and rocks as a storage medium. Compared to its alternatives, however, PBTES presents a limited flexibility of operation due to the conventional unidirectional flow, which involves the progressive reduction of the outlet temperature during discharge and thus lowers the thermodynamic efficiency of the power cycle. The present study summarizes the progress on the design and optimal operation of a novel multi-extraction PBTES, a project that aims at mitigating its typically poor operational flexibility for solar power applications. To this end, a one-dimensional model with a high spatial resolution of a PBTES was developed, which includes four intermediate outlet points along the axial direction to investigate the benefits of optimal extraction operation. In order to reduce the computational burden, a coarser model of the storage system is used in combination with non-linear model predictive control (NLMPC). Through the optimal manipulation of the extraction valves, the output temperature is maintained close to a prescribed temperature throughout the discharge. The control admits not only constant temperature targets, but also time-varying scheduled profiles. This work describes the limitation of such a design and control approach and sets the direction for the future, more detailed analyses needed to demonstrate its applicability.