We study eta(c) and J/psi hadroproduction induced by multiple scatteri
ng off fixed centers in the target. We determine the minimum number of
hard scatterings required and show that additional soft scatterings m
ay be factorized, at the level of the production amplitude for the eta
(c) and of the cross section for the J/psi. The J/psi provides an inte
resting example of soft rescattering effects occurring inside a hard v
ertex. We also explain the qualitative difference between the transver
se momentum broadening of the J/psi and of the Y observed in collision
s on nuclei. We point out that rescattering from spectators produced b
y beam and target parton evolution may have important effects on J/psi
production.