  We study the screening effect for the multiparton interactions (MPI) for
proton--deuteron collisions in the kinematics where one parton belonging to the
deuteron has small $x_1$ so the leading twist shadowing is present while the
second parton ($x_2$) is involved in the interaction %%ms in the kinematics
where shadowing effects are small. We find that the ratio of the shadowing and
the impulse approximation terms is approximately factor of two larger for MPI
than for the single parton distributions. We also calculate the double parton
antishadowing (DPA) contribution to the cross section due to the independent
interactions of the partons ofthe projectile proton with two nucleons of the
deuteron and find that shadowing leads to a strong reduction ofthe DPA
effect.For example, for the resolution scale $Q_1^2 \sim 4$~$\mbox{GeV}^2$ of
the interaction with parton $x_1$ we find that shadowing reduces the DPA effect
by $\sim$ 30%. It is argued that in the discussed kinematics the contribution
of interference diagrams, which correspond to the interchange ofpartonsbetween
the proton and neutron, constitutes only a small correction to the shadowing
contributions.
