External corporate governance mechanisms—such as shareholder engagement—exert increasing pressure on MNEs to address grand challenges, including fighting corruption, enabling good working conditions, and protecting human rights. While addressing grand challenges may require narrow scale solutions to address local specificities, shareholder engagement has become a global phenomenon. We study how investors can strategically balance issue scale framing with the institutional resources at their disposal and target MNEs’ capacity to address challenges. Empirically, we examine global shareholder engagement coordinated by the UN-supported Principles for Responsible Investment focused on MNEs’ solutions to grand challenges. We contribute to the literature on the importance of scale in relation to grand challenges by highlighting how investors’ framing of issue scale interacts with other factors for translation between local and global levels. Furthermore, we contribute to the literature on MNE capacity for addressing grand challenges by highlighting the contingencies for learning under opacity; and to the literature on comparative corporate governance by showing that investors need to strategically balance between institutional proximity with MNEs and the institutional diversity of their engagement coalitions. By doing so, we advance both theoretical and practical understandings of how complex configurations of external pressures contribute to MNEs adopting solutions to grand challenges.