  We systematically assess the DUNE experiment's ability to distinguish between
various beyond-standard neutrino oscillation hypotheses pair combinations. For
a pair comparison, we evaluate the statistical separation, where one hypothesis
plays the role of the true signal while the other corresponds to the test
signal. The beyond-standard neutrino oscillation hypotheses under scrutiny
include neutrino decay (invisible and visible), non-standard interactions,
quantum decoherence, and the violation of the equivalence principle. When taken
as the true model, we found that either quantum decoherence or the violation of
the equivalence principle are the easiest to differentiate compared to the rest
of the hypotheses. Additionally, from our statistical test, we investigate
potential discrepancies between the measured CP-violation phase $\delta_{CP}$
relative to its true value, which could occur for a given comparison. In our
analysis, we will take the true values of $\delta_{CP}$ as $-90^\circ$ and
$180^\circ$. Notably, even in cases where the beyond-standard neutrino
oscillation hypotheses scenarios are statistically indistinguishable, the
measured value can exhibit significant deviations from its true value.
