We search for tri-nucleon decays of ⁷⁶ Ge in the dataset from the GERmanium Detector Array (GERDA) experiment. Decays that populate excited levels of the daughter nucleus above the threshold for particle emission lead to disintegration and are not considered. The ppp-, ppn-, and pnn-decays lead to ⁷³ Cu, ⁷³ Zn, and ⁷³ Ga nuclei, respectively. These nuclei are unstable and eventually proceed by the beta decay of ⁷³ Ga to ⁷³ Ge (stable). We search for the ⁷³ Ga decay exploiting the fact that it dominantly populates the 66.7 keV ^73m Ga state with half-life of 0.5 s. The nnn-decays of ⁷⁶ Ge that proceed via ^73m Ge are also included in our analysis. We find no signal candidate and place a limit on the sum of the decay widths of the inclusive tri-nucleon decays that corresponds to a lower lifetime limit of 1.2 × 10 ²⁶ yr (90% credible interval). This result improves previous limits for tri-nucleon decays by one to three orders of magnitude.