  We study a three Higgs doublet model where one doublet is inert and the other
two doublets are active. Flavor changing neutral currents are avoided at
tree-level by imposing a softly broken $Z'_2$ symmetry and we consider type I
and type II Yukawa structures. The lightest inert scalar is a viable Dark
Matter (DM) candidate. A numerical scan of the free parameters is performed
taking into account theoretical constraints such as positivity of the scalar
potential and unitarity of $2 \rightarrow 2$ scattering amplitudes. The model
is further constrained by experimental results such as $B$ physics lower limits
on charged Higgs masses, Electroweak Precision Observables, LEP II, LHC Higgs
measurements, Planck measurement of the DM relic abundance and WIMP direct
searches by the LUX and XENON1T experiments. The model predictions for
mono-jet, mono Z and mono Higgs final states are studied and tested against
current LHC data and we find the model to be allowed. We also discuss the
effects of abandoning the "dark democracy" assumption common in studies of
inert models. Projected sensitivities of direct detection experiments will
leave only a tiny window in the DM mass versus coupling plane that is compliant
with relic density bounds.
