Solar geoengineering maintains a vocal presence as a stop-gap measure in assessments of climate and sustainability action. In this paper, we map prospective benefits and risks, and corresponding governance approaches, regarding three major proposals for solar geoengineering (stratospheric aerosol injection, marine cloud brightening, and a space-based sunshield). We do so by engaging with 44 focus groups conducted in 22 countries split between the global North and South. We compare results against previous research on the public perceptions of solar geoengineering as well as wider activities in assessment, innovation, and decision-making. We find that global South groups exhibit greater hope but an arguably richer range of concerns for solar geoengineering, in the context of observable inequities in climate action and potential geopolitical conflict. Meanwhile, a strong, global preference for multilateral coordination and public engagement from the conduct of research onwards is offset by skepticism of effective multilateralism and public discourse.