The search for relativistic scattering signals of cosmogenic light dark matter at terrestrial detectors has received increasing attention as an alternative approach to probe dark-sector physics. Large-volume neutrino experiments are well motivated for searches of dark matter that interacts very weakly with Standard Model particles and/or that exhibits a small incoming flux. We perform a dedicated signal sensitivity study for a detector similar to the one proposed by the DUNE Collaboration for cosmogenic dark-matter signals resulting from a non-minimal multi-particle dark-sector scenario. The liquid argon time projection chamber technology adopted for the DUNE detectors is particularly suited for searching for complicated signatures owing to good measurement resolution and particle identification, as well as $dE/dx$ measurements to recognize merged tracks. Taking inelastic boosted dark matter as our benchmark scenario that allows for multiple visible particles in the final state, we demonstrate that the DUNE far detectors have a great potential for probing scattering signals induced by relativistic light dark matter. Detector effects and backgrounds have been estimated and taken into account. Model-dependent and model-independent expected sensitivity limits for a DUNE-like detector are presented.
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