The textsc{Majorana Demonstrator} is an ultra low-background experiment searching for neutrinoless double-beta decay in $^{76}$Ge. The heavily shielded array of germanium detectors, placed nearly a mile underground at the Sanford Underground Research Facility in Lead, South Dakota, also allows searches for new exotic physics. Free, relativistic, lightly-ionizing particles with electrical charges less than $e$ are forbidden by the standard model but predicted by some of its extensions. If such particles exist, they might be detected in the textsc{Majorana Demonstrator} by searching for multiple- detector events with individual-detector energy depositions down to 1 keV. This search is background free and no candidate events have been found in 285 days of data taking. New direct-detection limits are set for the flux of lightly ionizing particles for charges as low as $e$/1000.
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