We present a stack of data from the second season of the CO Mapping Array Project (COMAP) on the positions of quasars from eBOSS and DESI. COMAP is a line intensity mapping (LIM) experiment targeting dense molecular gas via CO (1--0) emission at z box. We compare this upper limit to models of the CO emission stacked on quasars and find a tentative (∼ 3 σ) tension between the limit and the brightest stack models after accounting for a suite of additional sources of experimental attenuation and uncertainty, including quasar velocity uncertainty, pipeline signal loss, cosmic variance, and interloper emission in the LIM data. The COMAP-eBOSS/DESI stack is primarily a measurement of the CO luminosity in the quasars' wider environment, and is therefore potentially subject to environmental effects such as feedback. With our current simple models of the galaxy-halo connection, we are thus unable to confidently rule out any models of cosmic CO with the stack alone. Conversely, the stack's sensitivity to these large-scale environmental effects has the potential to make it a powerful tool for galaxy formation science, once we are able to constrain the average CO luminosity via the auto-power spectrum (a key goal of COMAP). Season 2 of COMAP represents a factor of three increase in map-level sensitivity over the previous early science data release. We do not detect any CO emission in the stack; instead, we find an upper limit of 10. 0 at 95% confidence within an ∼ 18 10^ 10 K km -1 pc² cMpc
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