  Through mean-field calculations, we demonstrate that, in a large $Z$ nucleus
binding multiple muons, these heavy leptons localize within a few dozen
femtometers of the nucleus. The mutual Coulomb interactions between the muons
and the protons can lead to a substantial decrease in proton chemical
potential, surpassing 1 MeV. These findings allow for expanding the
proton-dripline on the nuclear chart in principle, suggesting the possible
production of nuclei with Z around 120.
