In recent years, shareholder driven climate activism has focused attention on “universal owners and managers” – asset owners and managers with significant stakes in all or nearly all public companies. Advocates push these asset managers to prioritize enhancing overall portfolio value over maximizing individual company value, promoting "systemic stewardship" even when it involves sacrificing individual firm value for the benefit of the overall portfolio. This chapter assesses whether universal owners can and should pursue such a strategy. Our analysis is pessimistic for three main reasons. First, inducing individual portfolio firms to reduce their carbon output to address environmental concerns may trigger a competitive response that will reduce gains for other portfolio companies. Second, current corporate law has a "single firm focus" that conflicts with the potential "multi-firm focus" of large portfolio investors and exposes corporate fiduciaries to potential liability if they sacrifice firm value for the benefit of investors’ other holdings. Third, universal owners, managing diverse portfolios for various clients, face conflicts with fiduciary duties and their multi-client business model when implementing a tradeoff strategy. Given these challenges, systemic stewardship strategies that entail substantial tradeoffs are unlikely to have any significant impact on mitigating climate change.