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.
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