We study a model with three scalar doublets (3HDM) with an unbroken Z_2 symmetry where one of two of the doublets do not acquire a vev and hence are inert, so the lightest inert state becomes a dark matter candidate. For the version with one inert doublet, the I(1+2)HDM, we calculated the one-loop induced trilinear vertex HWZ and show that the dominant factor of the vertex gets an enhancement in comparison with the 2HDM due to the extra inert scalars running in the loop. For the model with two inert doublets, the I(2+1)HDM, we show that allowing a CPV phase in the inert sector opens new region of DM relic density compared with a CP-conserving model. We also analysed signals of DM production in the LHC, the heavy inert states can decay into the lightest producing a cascade decay of the Higgs boson with a large missing energy final state. This is a smoking-gun signal of the 3HDM since it is not allowed in the 2HDM with one inert doublet. Slide can be found here.