  In high energy nuclear collisions, the Glauber model is commonly used to
evaluate $J/\psi$ suppression due to 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 conclude that the related corrections are important to explain the
effective value extrapolated from experiment.
