  The high-$\mu_{\rm B}$ region of the QCD phase diagram has become the object
of several studies, focused on the investigation of the order of the phase
transition and the search for the critical point. Accessing rare probes is
experimentally challenging as it requires large integrated luminosities, and a
fixed-target environment represents an ideal solution for these studies. The
CERN SPS covers, with large beam intensity, the collision energy region
$5<\sqrt{s_{\rm NN}}<17$ GeV. A future experiment, NA60+, is being proposed to
access this region and perform accurate measurements of the dimuon spectrum
from threshold up to the charmonium mass region, and of hadronic decays of
charm and strange hadrons. The experiment, which is also part of the Physics
Beyond Colliders CERN initiative, aims at taking its first data with Pb and
proton beams around 2029.
