We present the first detailed phenomenological analysis of a radiative Majorana neutrino mass model constructed from opening up a ∆L = 2 mass-dimension-11 effective operator constructed out of standard model fields. While three such operators are generated, only one dominates neutrino mass generation, namely O 47 = L C LQ C QQQ C HH, where L denotes lepton doublet, Q quark doublet and H Higgs doublet. The underlying renormalisable theory contains the scalars S 1 ∼ (3, 1, 1/3) coupling as a diquark, S 3 ∼ (3, 3, 1/3) coupling as a leptoquark, and Φ 3 ∼ (3, 3, 2/3), which has no Yukawa couplings but does couple to S 1 and S 3 in addition to the gauge fields. Neutrino masses and mixings are generated at two-loop order. A feature of this model that is different from many other radiative models is the lack of proportionality to any quark and charged-lepton masses of the neutrino mass matrix. One consequence is that the scale of new physics can be as high as 10 7 TeV, despite the operator having a high mass dimension. This raises the prospect that ∆L = 2 effective operators at even higher mass dimensions may, when opened up, produce phenomenologically-viable radiative neutrino mass models. The parameter space of the model is explored through benchmark slices that are subject to experimental constraints from charged lepton flavour-violating decays, rare meson decays and neutral-meson mixing. The acceptable parameter space can accommodate the anomalies in R K ( * ) and the anomalous magnetic moment of the muon.