Theoretical limits imposed from halo abundances of the most massive plausible galaxies at a given epoch and volume within the extreme value statistics (EVS) formalism. The colored regions indicate the EVS confidence intervals for the COSMOS-Web survey area of 0.43 deg². The dotted line marks the median of the EVS distribution of the maximum plausible stellar mass, assuming a log-normal distribution of the SFE centered at ∼0.14, while the dashed line shows the 3σ upper limit assuming a SFE of unity. The grayscale hex bin histogram shows the M_⋆ − z_phot distribution of the full sample. Above the median $M_{\star }^{\max }$, the points mark individual galaxies in blue; those that have MIRI photometry are colored orange, and submillimeter detected sources are marked with yellow. The observed M_⋆ are corrected for the Eddington bias using Eq. (10). We find several candidates that are within the 2 and 3σ upper limits from the EVS as exceptionally massive for their epoch and volume. We mark submillimeter detected galaxies that are highly dust-attenuated with discrepant z_phot and M_⋆ solutions when including FIR-to-radio data in the SED fitting.