Future decarbonized applications that rely on renewable and carbon-dioxide-neutral hydrogen production could benefit from the gasification of waste to produce hydrogen. In the current study, an Aspen Plus® model was developed by coupling a co-gasification model to a water–gas shift (WGS) model. The feedstock employed in the simulations was a blend of municipal solid waste (MSW) and biomass from Morocco. A parametric assessment was conducted to analyze the effect of the steam-to-feedstock ratio (SFR) on the syngas composition and the WGS reactor temperature. This study also presents a comparison between the results of the gasification process before and after the WGS reactor, using air and steam as the gasifying agent. The results show an increase in hydrogen volumetric percentage for higher steam-to-feedstock ratios in the gasifier. Moreover, the inclusion of a WGS reactor enhances hydrogen and carbon dioxide while reducing the amount of carbon monoxide in the syngas for both air and steam as the gasifying agents. It can be concluded that a co-gasification process can be intensified by coupling it to a WGS reactor without steam injection to produce hydrogen-rich syngas with reduced operational expenditures.