A new heavy-ion experiment on fixed target, NA60+, has been proposed at the CERN SPS for data taking in the next years. Its main goals will be focused on precision studies of thermal dimuons, heavy quark and strangeness production in Pb-Pb collisions at center-of-mass energies ranging from 5 to 17 GeV, which will provide a unique opportunity to investigate the region of the QCD phase diagram at high baryochemical potential ($mu_B sim 200-400$~MeV). The key points of the NA60+ very broad and ambitious physics program will be described.
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