  We discuss the production of $D$-mesons and $J/\psi$ in high multiplicity
proton-proton and proton-nucleus collisions within the Color-Glass-Condensate
(CGC) framework. We demonstrate that the modification of the LHC data on $D$
and $J/\psi$ yields in high multiplicity events relative to minimum bias events
arise from a significant enhancement of the gluon saturation scales of the
corresponding rare parton configurations in the colliding protons and nuclei.
For a given event multiplicity, we predict these relative yields to be energy
independent from $\sqrt{s}=200$ GeV at RHIC to the highest LHC energies.
