We extend previous calculations of large-transverse-momentum $\ensuremath{\psi}$ and $\ensuremath{\Upsilon}$ production to Superconducting Super Collider energies. We then consider $\ensuremath{\psi}\ensuremath{\psi}$, $\ensuremath{\Upsilon}\ensuremath{\Upsilon}$, and $\ensuremath{\psi}\ensuremath{\Upsilon}$ production, both from the lowest-order (single-parton-interaction) gluon-fusion diagrams and from multiple-parton interactions. Finally, we discuss combined quarkonium and weak-boson production arising from both single- and multiple-parton interactions. Standard-model $W\ensuremath{\psi}$ and $W\ensuremath{\Upsilon}$ production is a potential background to the detection of charged Higgs bosons through their rare decays ${H}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{W}^{\ifmmode\pm\else\textpm\fi{}}V$.