The MAJORANA DEMONSTRATOR is searching for double-beta decay of $^{76}$Ge to excited states (E.S.) in $^{76}$Se using a modular array of high purity Germanium detectors. $^{76}$Ge can decay into three E.S.s of $^{76}$Se. The E.S. decays have a clear event signature consisting of a $betabeta$-decay with the prompt emission of one or two $gamma$-rays, resulting in with high probability in a multi-site event. The granularity of the DEMONSTRATOR detector array enables powerful discrimination of this event signature from backgrounds. Using 21.3 kg-y of isotopic exposure, the DEMONSTRATOR has set world leading limits for each E.S. decay, with 90% CL lower half-life limits in the range of $(0.56-2.1)cdot10^{24}$ y. In particular, for the $2 u$ transition to the first $0^+$ E.S. of $^{76}$Se, a lower half-life limit of $0.68cdot10^{24}$ at 90% CL was achieved.