  Flavor symmetric model is one of the attractive Beyond Standard Models (BSMs)
to reveal the flavor structure of the Standard Model (SM). A lot of efforts
have been put into the model building and we find many kinds of flavor
symmetries and setups are able to explain the observed fermion mass matrices.
In this paper, we look for common predictions of physical observables among the
ones in flavor symmetric models, and try to understand how to test flavor
symmetry in experiments. Especially, we focus on the BSMs for leptons with
extra Higgs $SU(2)_L$ doublets charged under flavor symmetry. In many flavor
models for leptons, remnant symmetry is partially respected after the flavor
symmetry breaking, and it controls well the Flavor Changing Neutral Currents
(FCNCs) and suggests some crucial predictions against the flavor changing
process, although the remnant symmetry is not respected in the full lagrangian.
In fact, we see that $\tau^- \to e^+ \mu^- \mu^-$ $( \mu^+ e^- e^-)$ and $e^+
e^- \to \tau^+\tau^-$ $(\mu^-\mu^+)$ processes are the most important in the
flavor models that the extra Higgs doublets belong to triplet representation of
flavor symmetry. For instance, the stringent constraint from the $\mu \to e
\gamma$ process could be evaded according to the partial remnant symmetry. We
also investigate the breaking effect of the remnant symmetry mediated by the
Higgs scalars, and investigate the constraints from the flavor physics: the
flavor violating $\tau$ and $\mu$ decays, the electric dipole moments, and the
muon anomalous magnetic moment. We also discuss the correlation between FCNCs
and nonzero $\theta_{13}$, and point out the physical observables in the
charged lepton sector to test the BSMs for the neutrino mixing.
