  Following the discovery of a Higgs boson, there has been renewed interest in
the general 2-Higgs-Doublet Model (2HDM). A model with One Inert Doublet plus
One Higgs Doublet (I(1+1)HDM), where one of the scalar doublets is "inert"
(since it has no vacuum expectation value and does not couple to fermions) has
an advantage over the 2HDM since it provides a good Dark Matter (DM) candidate,
namely the lightest inert scalar. Motivated by the existence of three fermion
families, here we consider a model with two scalar doublets plus one Higgs
doublet (I(2+1)HDM), where the two scalar doublets are inert. The I(2+1)HDM has
a richer phenomenology than either the I(1+1)HDM or the 2HDM. We discuss the
new regions of DM relic density in the I(2+1)HDM with simplified couplings and
address the possibility of constraining the model using recent results from the
Large Hadron Collider (LHC) and DM direct detection experiments.
