We address the question of whether the upcoming generation of dark matter search experiments and colliders will be able to discover if the dark matter in the Universe has two components of weakly interacting massive particles (WIMPs). We outline a model-independent approach, and we study the specific cases of (1) direct detection with low-background 1 ton noble-gas detectors and (2) a 0.5 TeV center of mass energy electron-positron linear collider. We also analyze the case of indirect detection via two gamma-ray lines, which would provide a verification of such a discovery, although multiple gamma-ray lines can in principle originate from the annihilation of a single dark matter particle. For each search channel, we outline a few assumptions to relate the very small set of parameters we consider (defining the masses of the two WIMPs and their relative abundance in the overall dark matter density) with the relevant detection rates. We then draw general conclusions on which corners of a generic dual-component dark matter scenario can be explored with current and next generation experiments. We find that in all channels the ideal setup is one where the relative mass splitting between the two WIMP species is of order 1, and where the two dark matter components contribute in a ratio close to 1:1 to the overall dark matter content of the Universe. Interestingly, in the case of direct detection, future experiments might detect multiple states even if only ~ 10% of the energy-density of dark matter in the Universe is in the subdominant species.
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