  In high energy nuclear collisions, the conventional Glauber model is commonly
used to evaluate the contribution to $J/\psi$ suppression originating from the
inelastic interaction with colorless bound nucleons. This requires an effective
value for the $J/\psi$-nucleon absorption cross section which is larger than
theoretically expected. On the other hand, multiple nucleon-nucleon collisions
mediated by color exchange interactions, excite their color degrees of freedom.
We investigate the importance of this effect and find that these excited states
provide a larger cross section for $J/\psi$ absorption. We conclude that the
related corrections are important to explain the effective value extrapolated
from experiment.
