  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.
