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This small, low-mass, mid M dwarf is known to host an Earth-mass exoplanet with an orbital period of 11.2 days within the habitable zone, as well as a long-period planet candidate with an orbital period of close to 5 yr.<\/jats:p>\n<jats:p><jats:italic>Aims.<\/jats:italic> We report on the analysis of a large set of observations taken with the ESPRESSO spectrograph at the VLT aimed at a thorough evaluation of the presence of a third low-mass planetary companion, which started emerging during a previous campaign.<\/jats:p>\n<jats:p><jats:italic>Methods.<\/jats:italic> Radial velocities (RVs) were calculated using both a cross-correlation function (CCF) and a template matching approach. The RV analysis includes a component to model Proxima\u2019s activity using a Gaussian process (GP). 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