  In this article we propose a simple model which can provide a combined
explanation of the $Z\to b\bar b$ forward-backward asymmetry, the Cabibbo Angle
Anomaly (CAA), $\tau\to\mu\nu\nu$ and $b\to s\ell^+\ell^-$ data. This model is
obtained by extending the Standard Model (SM) by two heavy vector-like quarks
(an $SU(2)_L$ doublet (singlet) with hypercharge $-5/6$ (-1/3)), two new
scalars (a neutral and a singly charged one) and a gauged $L_\mu-L_\tau$
symmetry. The mixing of the new quarks with the SM ones, after electroweak
symmetry breaking, does not only explain $Z\to b\bar b$ data but also generates
a lepton flavour universal contribution to $b\to s\ell^+\ell^-$ transitions.
Together with the lepton flavour universality violating effect, generated by
loop-induced $Z^\prime$ penguins involving the charged scalar and the heavy
quarks, it gives an excellent fit to data ($6.1\,\sigma$ better than the SM).
Furthermore, the charged scalar (neutral vector) gives a necessarily
constructive tree-level (loop) effect in $\mu\to e\nu\nu$ ($\tau\to
\mu\nu\nu$), which can naturally account for the CAA (${\rm
Br}[\tau\to\mu\nu\nu]/{\rm Br}[\tau\to e\nu\nu]$ and ${\rm
Br}[\tau\to\mu\nu\nu]/{\rm Br}[\mu\to e\nu\nu]$).
