  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.
