  We present a detailed study of a combined singlet-doublet scalar and
singlet-doublet fermion model for dark matter. These models have only been
studied separately in the past. We show that their combination allows for the
radiative generation of neutrino masses, but that it also implies the existence
of lepton-flavour violating (LFV) processes. We first analyse the dark matter,
neutrino mass and LFV aspects separately. We then perform two random scans for
scalar dark matter imposing Higgs mass, relic density and neutrino mass
constraints, one over the full parameter space, the other over regions where
scalar-fermion coannihilations become important. In the first case, a large
part of the new parameter space is excluded by LFV, and the remaining models
will be probed by XENONnT. In the second case, direct detection cross sections
are generally too small, but a substantial part of the viable models will be
tested by future LFV experiments. Possible constraints from the LHC are also
discussed.
