Coronal mass ejections (CMEs) expel multithermal, magnetized plasma from the Sun, and when directed toward Earth, can cause extensive damage to space and ground-based electronics. To better understand the triggering, acceleration, and evolution of CMEs, it is critical to study CME plasma properties close to the Sun. High-resolution ultraviolet and extreme ultraviolet (UV-EUV) spectroscopy can give the most detailed plasma diagnostics of CMEs in the low solar corona. Unfortunately, very few spectrally resolved observations of CMEs in the low solar corona exist. However, with the recent launch of the Spectral Imaging of the Coronal Environment on board Solar Orbiter and the upcoming missions, including the EUV High-Throughput Solar Telescope (EUVST) on Solar-C and the Multi-slit Solar Explorer (MUSE), we will have the opportunity to obtain unprecedented, spectrally resolved CME observations. Using the only full EUV spectral observation of a CME by the Hinode/EUV Imaging Spectrometer, we predict the spectra that SPICE, EUVST, and MUSE are expected to observe during an off-limb CME eruption to investigate the diagnostic capabilities of each instrument. Finally, we provide a list of density-sensitive and temperature-sensitive ratios for CME plasma diagnostics along with the expected spectral atlas for each instrument to facilitate observing sequence planning.