In this proceeding we present results of our studies of quarkonium
suppression in $pA$ collisions. We estimated the nuclear suppression
due to absorption, energy loss and gluon shadowing. In addition, we
found that at high energies a sizeable additive contribution comes
from multinucleon production. We demonstrate that the suggested approach can simultaneously explain a relatively small nuclear suppression of $J/\psi$ and $\Upsilon$, as well as a strong suppression of $\psi(2S)$ observed at RHIC and LHC in proton-ion collisions.