  We simultaneously investigate source, detector and matter non-standard
neutrino interactions at the proposed DUNE experiment. Our analysis is
performed using a Markov Chain Monte Carlo exploring the full parameter space.
We find that the sensitivity of DUNE to the standard oscillation parameters is
worsened due to the presence of non-standard neutrino interactions. In
particular, there are degenerate solutions in the leptonic mixing angle
$\theta_{23}$ and the Dirac CP-violating phase $\delta$. We also compute the
expected sensitivities at DUNE to the non-standard interaction parameters. We
find that the sensitivities to the matter non-standard interaction parameters
are substantially stronger than the current bounds (up to a factor of about
15). Furthermore, we discuss correlations between the source/detector and
matter non-standard interaction parameters and find a degenerate solution in
$\theta_{23}$. Finally, we explore the effect of statistics on our results.
