  Here, we propose a novel approach to experimentally and theoretically study
the properties of QCD matter under new extreme conditions, namely having an
initial temperature over 300~MeV and baryonic charge density over three times
the values of the normal nuclear density. According to contemporary theoretical
knowledge, such conditions were not accessible during the early Universe
evolution and are not accessible now in the known astrophysical phenomena. To
achieve these new extreme conditions, we proposed performing high-luminosity
experiments at LHC or other colliders by means of scattering the two colliding
beams at the nuclei of a solid target that is fixed at their interaction
region. Under plausible assumptions, we estimate the reaction rate for the
p+C+p and Pb+Pb+Pb reactions and discuss the energy deposition into the target
and possible types of fixed targets for such reactions. To simulate the triple
nuclear collisions, we employed the well-known UrQMD 3.4 model for the beam
center-of-mass collision energies 2.76 TeV. As a result of our modeling, we
found that, in the most central and simultaneous triple nuclear collisions, the
initial baryonic charge density is approximately three times higher than the
one achieved in the ordinary binary nuclear collisions at this energy.
