Cavity-mediated cooling has emerged as the only general technique with the potential to cool molecular species down to the microkelvin temperatures needed for quantum coherence and degeneracy. The EuroQUAM CMMC project will link leading theoreticians and experimentalists, including the technique's inventors and experimental pioneers, to develop it into a truly practical technique, reinforcing European leadership in this field. Four major experiments will explore a spectrum of complementary configurations and cavity-mediated cooling will be applied to molecules for the first time; a comprehensive theoretical programme will meanwhile examine the underlying mechanisms and identify the optimal route to practicality. The close connections between theory and experiment, and between pathfinding and underpinning studies, will allow each to guide and inform the others, ensuring that cavity-mediated cooling is swiftly developed as a broad enabling technology for new realms of quantum coherent molecular physics and chemistry.Collective cooling schemes have already been proposed for the strong coupling regime. The aim of the Leeds research is to develop a detailed theory for the collective cooling of particles trapped inside a highly leaky optical cavity. The theoretical results obtained for this so-called bad-cavity regime will be compared with the still unexplained experimental studies reported elsewhere. Moreover, they will provide concrete input in the design of the physical setups used by the experimental groups in this network, who will operate their cavity in the so-called bad cavity limit.