  In this letter, we study the potential of boosting the atmospheric neutrino
experiments sensitivity to the neutrino mass ordering (NMO) sensitivity by
incorporating inelasticity measurements. We show how this observable improves
the sensitivity to the NMO and the precision of other neutrino oscillation
parameters relevant to atmospheric neutrinos, specifically in the
IceCube-Upgrade and KM3NeT-ORCA detectors. Our results indicate that an
oscillation analysis of atmospheric neutrinos including inelasticity
information has the potential to enhance the ordering discrimination by several
units of $\chi^2$ in the assumed scenario of 5 and 3 years of running of
IceCube-Upgrade and KM3NeT-ORCA detectors, respectively.
