While raising concerns, the recent proliferation of grand challenges has sparked interest in the role played by innovation in causing them, and in how the attempts made to fix them may cause even greater challenges that present themselves down the line. This article provides an analysis of the bibliographic metadata, published between 2002 and 2020, focusing explicitly on the private‐for‐profit sector. By identifying common themes from 66 documents, a framework highlighting the shared concerns and research trajectories was derived. Our results are illustrated and discussed along 11 research themes. We contribute theoretically by identifying the innovation efforts of for‐profit firms that directly relate to grand challenges, through two cases of carbon capture and storage and deep‐sea mining. We conclude that a more holistic understanding of innovation and its many possible consequences needs to be developed. We highlight the limitations of perspectives that do not always take full account of the potential divergence of interests between stakeholders, and, how fuller input by a greater cross‐section of stakeholders may help identify any negative effects of innovations at an earlier stage. Informed by recent extensions of social innovation theory, we explore the potential for synthesis around a pragmatic understanding of institutions, stakeholders, and the nature and quality of ties that bind them.