When the singlet-doublet fermion dark matter model is extended with additional $Z_2$--odd real singlet scalars, neutrino masses and mixings can be generated at one-loop level. In this work, we discuss the salient features arising from the combination of the two resulting simplified dark matter models. When the $Z_2$-lightest odd particle is a scalar singlet, $\operatorname{Br}(\mu\to e \gamma)$ could be measurable provided that the singlet-doublet fermion mixing is small enough. In this scenario, also the new decay channels of vector-like fermions into scalars can generate interesting leptonic plus missing transverse energy signals at the LHC. On the other hand, in the case of doublet-like fermion dark matter, scalar coannihilations lead to an increase in the relic density which allow to lower the bound of doublet-like fermion dark matter.