  The joint study of Double Parton Scatterings, in high energy proton-proton
and proton-nucleus collisions, can provide a lot of information on multi-parton
correlations. The multi-parton structure is in fact probed in a different way
by DPS, in $p$-$p$ and in $p$-$A$ collisions. In $p$-$A$ collisions the
interpretation of the experimental results may be however complicated by the
presence of interference terms, which are missing in $p$-$p$. A suitable
reaction channel, where interference terms are absent, is $WJJ$ production. By
studying $WJJ$ production in $p$-$Pb$ collisions, we estimate that the fraction
of events due to DPS may be larger by a factor 3 or 4, as compared to $p$-$p$,
while the amount of the increased fraction can give a direct indication on the
importance of different correlation terms.
