We initiate the study of novel thermal dark matter (DM) scenarios where the DM annihilation today produces boosted stable particles in the dark sector, which can be a subdominant DM component. The same annihilation in the early universe also sets the thermal relic abundance of the DM, and provides a natural, alternative way to preserve WIMP DM miracle while being compatible with existing constraints from DM detections. We consider the cases where the boosted DM coming from the galactic centre and from the Sun. The boosted DM can be detected at large volume terrestrial experiments via neutral-current-like interactions with electrons or nuclei, for instance at experiments designed for neutrino physics or proton decay, in particular Super-K/Hyper-K as well as IceCube/PINGU. We study the sensitivities of these experiments for boosted DM signals from example models. This boosted DM phenomenon highlights the distinctive signatures possible from non-minimal dark sectors.