We consider the doublet-triplet fermionic model in the scheme of the custodial limit when the dark matter (DM) candidate is pure doublet and lies at the electroweak scale. This scheme, despite being an appealing and promising DM model, is severely constrained by the interplay between the DM relic density constraint and the LHC measurement of the Higgs diphoton decay rate. In this work, the DM relic density is considered to arise from either a nonstandard cosmology scenario or as a part of a larger sector encompassing other DM particles in order to saturate the observed relic abundance. For these scenarios we investigate the impact of the new sector in different collider observables, and study constraints coming from direct detection and indirect detection of gamma-rays both in the diffuse and linelike spectrum. As a result, we find that in the nonstandard cosmology scenario most experiments impose, up to a certain point, restrictions, though large portions of the parameter space are still viable. For the multi-component case, only direct detection imposes constraints.