  We argue that the observation of the color transparency effect in the
semiexclusive $A(\pi^-,l^+ l^-)$ process is important for determining whether
it is possible to extract the generalized parton distributions of the nucleon
from the elementary reaction $\pi^- p \to l^+ l^- n$ at $p_{\rm lab}=15-20$
GeV/c at small $|t|$ and large invariant mass of the dilepton pair $l^+ l^-$.
Assuming that the transverse size of the pionic $q \bar q$ pair in the hard
interaction point is similar to the one in the reaction $\gamma^* p\to \pi^+ n$
studied at JLab we predict large color transparency effects in the discussed
kinematic range. We also suggest that the semiexclusive $\rho^0$ production in
$\pi^-$-induced reactions in the same beam momentum region may provide new
information on the dynamics of the interaction in the non-vacuum channel, while
the $J/\psi$ production can be used to get information on $J/\psi N$ total
interaction cross section.,
