  We discuss the constraints and phenomenology of the $Z_2 \times Z_2$ three
Higgs doublet model (3HDM) with two inert scalars, originating two dark matter
(DM) particles. We elucidate the competing vacua and we submit the model to all
theoretical and current experimental constraints. We find unexplored regions of
parameter space and investigate their experimental signatures. In particular,
we find regions where the two DM particles contribute equally to the relic DM
density.
