  The 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. We present the first limits for tri-nucleon decay-specific
modes and invisible decay modes for Ge isotopes. We find a half-life limit of
$4.9 \times 10^{25}$ yr for the decay $^{76}{\rm Ge(ppn)} \to {}^{73}{\rm Zn}\
e^+\pi^+$ and $4.7\times10^{25}$ yr for the decay $^{76}{\rm Ge(ppp)} \to
^{73}{\rm Cu}\ e^+\pi^+\pi^+$. The half-life limit for the invisible tri-proton
decay mode of $^{76}$Ge was found to be $7.5\times10^{24}$ yr.
