We report the realisation of a high-finesse open-access cavity array, tailored towards the creation of multiple coherent light-matter interfaces within a compact environment. We describe the key technical developments put in place to fabricate such a system, comprising the creation of tapered pyramidal substrates and an in-house laser machining setup. Cavities made from these mirrors are characterised, by laser spectroscopy, to possess similar optical properties to state-of-the-art fibre-tip cavities, but offer a compelling route towards improved performance, even when used to support only a single mode. The implementation of a 2×2 cavity array and the independent frequency tuning between three neighbouring sites are demonstrated.