We present the opto-mechanical design of GMOX, the Gemini Multi-Object eXtra-wide-band spectrograph, a potential next-generation (Gen-4 #3) facility-class instrument for Gemini. GMOX is a wide-band, multi-object, spectrograph with spectral coverage spanning 350 nm to 2.4 um with a nominal resolving power of R 5000. Through the use of Digital Micromirror Device (DMD) technology, GMOX will be able to acquire spectra from hundreds of sources simultaneously, offering unparalleled flexibility in target selection. Utilizing this technology, GMOX can rapidly adapt individual slits to either seeing-limited or diffraction-limited conditions. The optical design splits the bandpass into three arms, blue, red, and near infrared, with the near-infrared arm being split into three channels covering the Y+J band, H band, and K band. A slit viewing camera in each arm provides imaging capability for target acquisition and fast-feedback for adaptive optics control with either ALTAIR (Gemini North) or GeMS (Gemini South). Mounted at the Cassegrain focus, GMOX is a large (1.3 m x 2.8 m x 2.0 m) complex instrument, with six dichroics, three DMDs (one per arm), five science cameras, and three acquisition cameras. Roughly half of these optics, including one DMD, operate at cryogenic temperature. To maximize stiffness and simplify assembly and alignment, the opto-mechanics are divided into three main sub-assemblies, including a near-infrared cryostat, each having sub-benches to facilitate ease of alignment and testing of the optics. In this paper we present the conceptual opto-mechanical design of GMOX, with an emphasis on the mounting strategy for the optics and the thermal design details related to the near-infrared cryostat.