  We provide a first study of Mellin moments of double parton distributions
(DPDs) in the nucleon on the lattice, where we consider several combinations of
quark flavors and polarizations. These are accessible through two-current
correlations, which can be obtained by evaluating four-point functions. In this
context we consider all possible Wick contractions, where for almost all of
them sufficiently clear signals are obtained. In the present study, we employ
an $n_f = 2 + 1$ CLS ensemble on a $96 \times 32^3$ lattice with lattice
spacing $a = 0.0856\ \mathrm{fm}$ and the pseudoscalar masses $m_\pi = 355\
\mathrm{MeV}$ and $m_K = 441\ \mathrm{MeV}$.
