  Next generation neutrino oscillation experiments like DUNE and T2HK are
multi-purpose observatories, with a rich physics program beyond oscillation
measurements. A special role is played by their near detector facilities, which
are particularly well-suited to search for weakly coupled dark sector particles
produced in the primary target. In this paper, we demonstrate this by
estimating the sensitivity of the DUNE near detectors to the scattering of
sub-GeV DM particles and to the decay of sub-GeV sterile neutrinos ("heavy
neutral leptons"). We discuss in particular the importance of the DUNE-PRISM
design, which allows some of the near detectors to be moved away from the beam
axis. At such off-axis locations, the signal-to-background ratio improves for
many new physics searches. We find that this leads to a dramatic boost in the
sensitivity to boosted DM particles interacting mainly with hadrons, while for
boosted DM interacting with leptons, data taken on-axis leads to marginally
stronger exclusion limits. Searches for heavy neutral leptons perform equally
well in both configurations.
