  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.
