By extending the Standard Model with three right-handed neutrinos (Ni) and a second Higgs doublet (H2), odd under a Z2 symmetry, it is possible to explain non-zero neutrino masses and to account for the dark matter. We consider the case where the dark matter is a scalar and study its coannihilations with the right-handed neutrinos. These coannihilations tend to increase, rather than reduce, the dark matter density and they modify in a significant way the viable parameter space of the model. In particular, they allow to satisfy the relic density constraint for dark matter masses well below 500 GeV. The dependence of the relic density on the relevant parameters of the model, such as the dark matter mass, the mass splitting, and the number of coannihilating fermions, is analyzed in detail. We also investigate, via a scan over the parameter space, the new viable regions that are obtained when coannihilations are taken into account. Notably, they feature large indirect detection rates, with ⟨σv⟩ reaching values of order 10−24cm3s−1. Finally, we emphasize that coannihilation effects analogous to those discussed here can be used to reconcile a thermal freeze-out with a large ⟨σv⟩ also in other models of dark matter.