  In this letter we show that the two parton showers mechanism for $J/\Psi$
production, that has been discussed in Ref.[28], leads to small values of
$\sigma_{\rm eff}$ for the production of a pair of $J/\Psi$. We develop a
simple two channel approach to estimate the values of $\sigma_{\rm eff}$, which
produces values that are in accord with the experimental data.
