  Motivated by the ion-collision program at the Large Hadron Collider, plans
for its high-luminosity upgrade, and on-going discussions for multi-TeV future
hadron colliders, we systematically investigate hard-scattering, Standard Model
processes in many-TeV ion-ion collisions. We focus on the symmetric beam
configurations $^{208}$Pb-$^{208}$Pb, $^{131}$Xe-$^{131}$Xe, $^{12}$C-$^{12}$C,
and $pp$, and we catalog total and fiducial cross sections for dozens of
processes, ranging from associated-Higgs and multiboson production to
associated-top pair production, at next-to-leading order in QCD for
nucleon-nucleon collision energies from $\sqrt{s_{NN}}=1$ to $100$ TeV. We
report the residual scale uncertainties at this order as well as the
uncertainties originating from fits of nuclear parton densities. We also
discuss the propagation of nuclear dynamics (as encoded in nuclear parton
densities) into parton luminosities, and ultimately into predictions for cross
sections. Finally, we report on the emergence of trends and the reliability of
extrapolating cross sections across different nuclei.
