We present a scotogenic model, i.e. a one-loop neutrino mass model with dark right-handed neutrino gauge singlets and one inert dark scalar gauge doublet $eta$, which has symmetries that lead to co-bimaximal mixing, i.e. to an atmospheric mixing angle $theta_{23} = 45^circ$ and to a $CP$-violating phase $delta = pm pi/2$, while the mixing angle $theta_{13}$ remains arbitrary. The symmetries consist of softly broken lepton numbers $L_alpha$ ($alpha = e,mu,tau$), a non-standard $CP$ symmetry, and three $Z_2$ symmetries. We indicate two possibilities for extending the model to the quark sector. Since the model has, besides $eta$, three scalar gauge doublets, we perform a thorough discussion of its scalar sector. We demonstrate that it can accommodate a Standard Model-like scalar with mass $125, mathrm{GeV}$, with all the other charged and neutral scalars having much higher masses.
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