  We develop a framework and unified, compact notation to include neutrino
direct interaction effects with neutrino oscillations for a wide class of
low-energy, effective four-Fermi interactions. Modest flavor-violating
interaction strengths can make significant changes in the boundaries in $\Delta
M^2 \leftrightarrow sin^2 2\theta$ and in $tan^2 \theta_{13} \leftrightarrow
tan^2 \theta_{23} parameter space. We draw examples from the L-R symmetric and
$MSSM + \slash R$ models and find the recently reported decay-at-rest $\mu
\leftrightarrow e$ transition probability can be described without oscillations
in L-R symmetric models.
