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In this article we propose a simple model which can provide a combinedexplanation of the $Z\to b\bar b$ forward-backward asymmetry, the Cabibbo AngleAnomaly (CAA), $\tau\to\mu\nu\nu$ and $b\to s\ell^+\ell^-$ data. This model isobtained 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 newscalars (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 electroweaksymmetry breaking, does not only explain $Z\to b\bar b$ data but also generatesa lepton flavour universal contribution to $b\to s\ell^+\ell^-$ transitions.Together with the lepton flavour universality violating effect, generated byloop-induced $Z^\prime$ penguins involving the charged scalar and the heavyquarks, it gives an excellent fit to data ($6.1\,\sigma$ better than the SM).Furthermore, the charged scalar (neutral vector) gives a necessarilyconstructive tree-level (loop) effect in $\mu\to e\nu\nu$ ($\tau\to\mu\nu\nu$), which can naturally account for the CAA (${\rmBr}[\tau\to\mu\nu\nu]/{\rm Br}[\tau\to e\nu\nu]$ and ${\rmBr}[\tau\to\mu\nu\nu]/{\rm Br}[\mu\to e\nu\nu]$).

Combined Explanation of the $Z\to b\bar b$ Forward-Backward Asymmetry, the Cabibbo Angle Anomaly, $\tau\to\mu\nu\nu$ and $b\to s\ell^+\ell^-$ Data