Non-minimal $331$ model for Lepton Flavour Universality Violation in $b\to s\ell\ell$ decays

331 models constitute an extension of the Standard Model (SM) obtained by enlarging the SM gauge group $SU(3)_\text{C}\times SU(2)_\text{L}\times U(1)_Y$ to the group $SU(3)_\text{C}\times SU(3)_\text{L}\times U(1)_X$. We investigate how a non-minimal 331 model may embed lepton flavour universality violating contributions to $b\to s\ell\ell$ processes without introducing lepton flavour violation, as suggested by the recent LHCb measurements of the ratios $R_K$ and $R_{K^*}$. We discuss the model-independent scenarios of New Physics in $b\to s\ell\ell$ currently favoured by the data that could be accommodated by this model and consider a few phenomenological constraints on this model.