  We present a model for Lepton Flavor Violating (LFV) neutral current
non-standard interactions of neutrinos with matter fields parameterized by
$\epsilon_{\alpha \beta}^f$ with $\alpha \ne \beta$. Here, unlike the previous
models, the ratios of the off-diagonal LFV elements of the effective NSI
coupling to the diagonal lepton flavor conserving ones ({\it i.e.,}
$(\epsilon_{\alpha \beta}^f)^2/(\epsilon_{\alpha \alpha}^f \epsilon_{\beta
\beta}^f)$ ) are arbitrary. The model enjoys rich phenomenology, predicting
invisible Higgs decay and new meson decay modes observable in upcoming
experiments. The model for $\epsilon_{\mu e}^f$ also predicts a $\mu^-$ to
$e^-$ conversion rate on nuclei accessible in the planned experiments.
