AbstractAssuming confirmation of the anomalies in semi-leptonic B-decays, their explanation in terms of the exchange of a massive vector leptoquark field, $$U_{\mu }^a$$ U μ a , of charge 2/3, appears to require the inclusion of $$U_{\mu }^a$$ U μ a in the vector multiplet of the adjoint of Pati–Salam SU(4), $${\mathcal {G}}_{\mu }^A$$ G μ A , as well as the introduction of vector-like fermions, $$F_j$$ F j , in the fundamental of SU(4). We consider simplified models characterised by the nature of the SU(4) symmetry (global or local), by the number of vector-like fermions, and by the couplings of the Higgs boson to SM fermions (direct or induced by mixing with the vector-like fermions). In all cases, we implement a minimal breaking of a $$U(2)^n_f$$ U ( 2 ) f n flavour symmetry, with a single motivated exception. We then perform a global fit including the main observables sensitive to exchanges of the $${\mathcal {G}}_{\mu }^A$$ G μ A at tree level and in loops dominated by logs insensitive to the UV completion.