Not yet reviewed by Pith; the record is open.

Non-standard interactions (NSI) between neutrinos and matter at long-baseline experiments could make determination of the CP-violating phase $\delta_{13}$ ambiguous due to interference with additional complex phases. Such degeneracies are often studied in the context of specific experiments and a few parameter choices, leaving it unclear how to extract a general understanding of when two sets of parameters may be degenerate or how different types of experiments in principle combine to lift such a degeneracy. This work complements detailed simulations of individual experiments by showing how underlying parameters relate to degeneracies as represented on a biprobability plot. We show how a range of energies near the oscillation maximum $\Delta_{31} = \pi/2$ separates some degenerate probabilities along the CP-conserving direction of biprobability space according to $\delta_{+} \equiv \delta_{13} + \delta_{e\tau}$, while near $\Delta_{31} = 3\pi/2$ degenerate probabilities are separated along the CP-violating direction according to $\delta_{e\tau}$. We apply this to the experimental hints that suggest $\delta_{13} \sim -\pi/2$ to see that this could also be consistent with $\delta_{13}, \delta_{e\tau} = 0$ or $\pi$. The baseline and energy range characteristic of DUNE provides some resolution, but a further improvement comes from beams a few degrees off-axis at $\gtrsim 1000$ km baselines, including some proposed sites for T2HKK.