Bridging the long distances between different metropolitan-scale quantum networks is currently best achieved using satellites, which can cover thousands of kilometres. The development of efficient approaches to establish connectivity between ground nodes and a satellite is therefore an essential next step. We propose a network with dual-functionality: during a brief satellite pass, the ground network is configured as a multipoint-to-point topology where all ground nodes establish entanglement with a satellite receiver. During times when this satellite is not available, the satellite up-link is rerouted via a single optical switch to the ground nodes, and the network is configured as a pair-wise ground network. We numerically simulate a pulsed hyper-entangled photon source and study the performance of the proposed network configurations for quantum key distribution. We find favourable resource overheads in the case that the satellite receiver exploits time-multiplexing whereas the ground nodes utilize frequency-multiplexing. Our results show high and scalable key rates can be achieved in both configurations. The scalability, simple reconfigurability, and easy integration with fibre networks make this architecture a promising candidate for quantum communication of many ground nodes and a satellite thus paving the way towards interconnection of ground nodes at a global scale.