  We study a $Z_2 \times Z'_2$ symmetric 3-Higgs Doublet Model (3HDM), wherein
two of the doublets are inert and one is active (thus denoted in literature as
I(2+1)HDM), yielding a two-component Dark Matter (DM) sector. The two DM
candidates emerge as the lightest scalar component of a different inert
doublet, each with a different odd discrete parity, and cooperate to achieve
the correct relic density. When a sufficient mass difference exists between the
two DM candidates, it is possible to test the presence of both in present
and/or forthcoming facilities, as the corresponding masses are typically at the
electroweak scale. Specifically, the light DM component can be probed by the
nuclear recoil energy in direct detection experiments while the heavy DM
component appears through the photon flux in indirect detection experiments. In
fact, the DM mass sensitivity that the two experimental set-ups can achieve
should be adequate to establish the presence of two different DM signals. This
result has been obtained in the presence of a thorough theoretical analysis of
the stability conditions of the vacuum structure emerging from our I(2+1)HDM
construct, ensuring that the model configurations adopted are physical, and of
up-to-date constraints coming from data collected by both space and ground
experiments, ensuring that the coupling and mass spectra investigated are
viable phenomenologically.
