Flavourful $Z$ models for $R_{K^{(*)}}$

We show how any flavour conserving $Z$ model can be made flavour violating and non-universal by introducing mass mixing of quarks and leptons with a fourth family of vector-like fermions with non-universal $Z$ couplings. After developing a general formalism, we focus on two concrete examples, namely a fermiophobic model, and an $SO(10)$ GUT model, and show how they can account for the anomalous $B$ decay ratios $R_K$ and $R_{K^*}$. A similar analysis could be performed for $B-L$ models, $E_6$ models, composite models, and so on.