SOLPS-ITER modeling of EDA H-mode experiments on Alcator C-Mod find that the electron density pedestal structure is unaffected by increased gas fueling when approaching ITER-like opaqueness conditions. SOLPS-ITER simulations show a decrease in the neutral penetration depth with increasing pedestal density, similar to prior experiments (Hughes et al., 2006). Neutral density and penetration depth vary poloidally, and we show that the highest neutral densities at the separatrix are found closest to the gas puff locations both on the high field side and the low field side. The decrease in the neutral penetration depth with increasing pedestal density, as well as the decrease in the neutral density at the separatrix, are not just limited to the midplane, but persist at every poloidal location. We find, however, that when gas puffs of similar magnitude as those employed in experiments are added, a much larger increase in the electron density is observed over the whole modeled plasma radius. This does suggest that changes in transport will need to be included self-consistently. • SOLPS-ITER provides insight on the dynamics of neutrals in high opacity H-modes. • SOL neutral opacity can be quantified by radial neutral density e-folding length. • Density pedestal formation is mostly unaffected as pedestal opacity increases. increases. • High gas-puffing only moderately increases neutral penetration of the pedestal. • At high pedestal opacity, main chamber fueling dominates fueling through the X-point.