Theorists of transnational climate governance (TCG) seek to account for the increasing involvement of nonstate and substate actors in global climate policy. While transnational actors have been present in the emerging field of solar geoengineering—a novel technology intended to reflect a fraction of sunlight back to space to reduce climate impacts— many of their most significant activities, including knowledge dissemination, scientific capacity building, and conventional lobbying, are not captured by the TCG framework. Insofar as TCG is identified with transnational governance and transnational governance is important to reducing climate risks, an incomplete TCG framework is problematic for effective policy making. We attribute this shortcoming on the part of TCG to its exclusive focus on steering and corollary exclusion of influence as a critical component of governance. Exercising influence, for example, through inside and outside lobbying, is an important part of transnational governance—it complements direct governing with indirect efforts to inform, persuade, pressure, or otherwise influence both governor and governed. Based on an empirical analysis of solar geoengineering research governance and a theoretical consideration of alternative literatures, including research on interest groups and nonstate advocacy, we call for a broader theory of transnational governance that integrates steering and influence in a way that accounts for the full array of nonstate and substate engagements beyond the state.