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Abstract The persisting anomalous data in semileptonic B-decays point towards New Physics models exhibiting large sources of Lepton Flavour Universality Violation. In this work we generalise previous studies by considering frameworks which include an enlarged set of semileptonic four-fermion operators invariant under the SM gauge group, with New Physics affecting mainly the third generation. We derive the low-energy effective Lagrangian including the leading electroweak corrections, mandatory to obtain reliable predictions. As a particularly interesting case, we analyse the scenario where the dominant New Physics effects are encoded in the Wilson coefficient C 9, as favoured by global fit analyses of b → s data. We find that also in this case the stringent experimental bounds on Z-pole observables and τ decays challenge a simultaneous explanation of charged and neutral-current non-standard data.