Abstract We introduce COMAP-EoR, the next generation of the Carbon Monoxide Mapping Array Project aimed at extending CO intensity mapping to the Epoch of Reionization. COMAP-EoR supplements the existing 30 GHz COMAP Pathfinder with two additional 30 GHz instruments and a new 16 GHz receiver. This combination of frequencies will be able to simultaneously map CO(1–0) and CO(2–1) at reionization redshifts (z ∼ 5–8) in addition to providing a significant boost to the z ∼ 3 sensitivity of the Pathfinder. We examine a set of existing models of the EoR CO signal, and find power spectra spanning several orders of magnitude, highlighting our extreme ignorance about this period of cosmic history and the value of the COMAP-EoR measurement. We carry out the most detailed forecast to date of an intensity mapping cross correlation, and find that five out of the six models we consider yield signal to noise ratios (S/Ns) ≳ 20 for COMAP-EoR, with the brightest reaching a S/N above 400. We show that, for these models, COMAP-EoR can make a detailed measurement of the cosmic molecular gas history from z ∼ 2–8, as well as probe the population of faint, star-forming galaxies predicted by these models to be undetectable by traditional surveys. We show that, for the single model that does not predict numerous faint emitters, a COMAP-EoR-type measurement is required to rule out their existence. We briefly explore prospects for a third-generation Expanded Reionization Array (COMAP-ERA) capable of detecting the faintest models and characterizing the brightest signals in extreme detail.