The Gemini Infra-Red Multi-Object Spectrograph (GIRMOS) is a four-arm, Multi-Object Adaptive Optics (MOAO) IFU spectrograph being built for Gemini (commissioning in 2024). GIRMOS is being planned to interface with the new Gemini-North Adaptive Optics (GNAO) system, and is base lined with a requirement of 50% EE within a 0.10 '' spaxel at H-band. We present a design and forecast the error budget and performance of GIRMOS-MOAO working behind GNAO. The MOAO system will patrol the 20 field of regard of GNAO, utilizing closed loop GLAO or MCAO for lower order correction. GIRMOS MOAA will perform tomographic reconstruction of the turbulence using the GNAO WFS, and utilize order 16x16 actuator DMs operating in open loop to perform an additional correction from the Pseudo Open Loop (POL) slopes, achieving close to diffraction limited performance from the combined GNAO+MOAO correction. This high performance AO spectrograph will have the broadest impact in the study of the formation and evolution of galaxies, but will also have broad reach in fields such as star and planet formation within our Milky Way and supermassive black holes in nearby galaxies.