  We propose a simple model to simultaneously explain four observed flavor
anomalies while generating the neutrino mass at the one-loop level.
Specifically, we address the measured anomalous magnetic dipole moments of the
muon, $\Delta a_\mu$ , and electron, $\Delta a_e$, the observed anomaly of
$b\rightarrow s l^+ l^-$ in the $B$-meson decays, and the Cabibbo-angle
anomaly. The model consists of four colorful new degrees of freedom: three
scalar leptoquarks with the Standard Model quantum numbers
$(3,3,-1/3),(3,2,1/6)$, and $(3,1,2/3)$, and one pair of down-quark-like vector
fermion in $(3,1,-1/3)$. The baryon number is assumed to be conserved for
simplicity.
  Phenomenologically viable solutions with the minimal number of real
parameters can be found to accommodate all the above-mentioned anomalies and
produce the approximate, close to $1\sigma$, neutrino oscillation pattern at
the same time. From general consideration, the model robustly predicts: (1)
neutrino mass is of the normal hierarchy type, and (2) ${\cal
M}^\nu_{ee}\lesssim 3\times 10^{-4}\mbox{eV}$.
  The possible UV origin to explain the flavor pattern of the found viable
parameter space is briefly discussed. The parameter space can be well
reproduced within a simple split fermion toy model.
