  Neutrino non-standard interactions (NSI) with the first generation of
standard model fermions can span a parameter space of large dimension and
exhibit degeneracies that cannot be broken by a single class of experiment.
Oscillation experiments, together with neutrino scattering experiments, can
merge their observations into a highly informational dataset to combat this
problem. We consider combining neutrino-electron and neutrino-nucleus
scattering data from the Borexino and COHERENT experiments, including a
projection for the upcoming coherent neutrino scattering measurement at the
CENNS-10 liquid argon detector. We extend the reach of these data sets over the
NSI parameter space with projections for neutrino scattering at a future
multi-ton scale dark matter detector and future oscillation measurements from
atmospheric neutrinos at the Deep Underground Neutrino Experiment (DUNE). In
order to perform this global analysis, we adopt a novel approach using the
copula method, utilized to combine posterior information from different
experiments with a large, generalized set of NSI parameters. We find that the
contributions from DUNE and a dark matter detector to the Borexino and COHERENT
fits can improve constraints on the electron and quark NSI parameters by up to
a factor of 2 to 3, even when relatively many NSI parameters are left free to
vary in the analysis.
