Silicon nitride $({\mathrm{Si}}_3{\mathrm{N}}_4)\text{-}\mathrm{on}\text{-}{\mathrm{SiO}}_2$ attracts increasing interest in integrated photonics owing to its low propagation loss and wide transparency window, extending from $～400\mathrm{nm}$ to 2350 nm. Scalable integration of active devices such as amplifiers and lasers on the ${\mathrm{Si}}_3{\mathrm{N}}_4$ platform will enable applications requiring optical gain and a much-needed alternative to hybrid integration, which suffers from high cost and lack of high-volume manufacturability. We demonstrate a high-gain optical amplifier in ${\mathrm{Al}}_2{\mathrm{O}}_3\text{:}{\mathrm{Er}}^3$ monolithically integrated on the ${\mathrm{Si}}_3{\mathrm{N}}_4$ platform using a double photonic layer approach. The device exhibits a net ${\mathrm{Si}}_3{\mathrm{N}}_4\text{-}\mathrm{to}\text{-}{\mathrm{Si}}_3{\mathrm{N}}_4$ gain of $18.1\pm 0.9\mathrm{dB}$ at 1532 nm, and a broadband gain operation over 70 nm covering wavelengths in the S-, C- and L-bands. This work shows that rare-earth-ion-doped materials and in particular, rare-earth-ion-doped ${\mathrm{Al}}_2{\mathrm{O}}_3$, can provide very high net amplification for the ${\mathrm{Si}}_3{\mathrm{N}}_4$ platform, paving the way to the development of different active devices monolithically integrated in this passive platform.