  Neutrino oscillations induced by a flavor-dependent violation of the Einstein
Equivalence Principle (VEP) have been recently considered as a suitable
explanation of the solar electron-neutrino deficiency. Unlike the MSW
oscillation mechanism, the VEP mechanism is dependent on a coupling to the
local background gravitational potential $\Phi$. We investigate the differences
which arise by considering three-flavor VEP neutrinos oscillating against fixed
background potentials, and against the radially-dependent solar potential. This
can help determine the sensitivity of the gravitationally-induced oscillations
to both constancy and size (order of magnitude) of $\Phi$. In particular, we
consider the potential of the local superculster, $|\Phi|=3\times 10^{-5}$, in
light of recent work suggesting that the varying solar potential has no effect
on the oscillations. The possibility for arbitrarily large background
potentials in different cosmologies is discussed, and the effects of one such
potential ($\Phi = 10^{-3}$) are considered.
