Bank holding companies (BHCs) can be complex organizations, conducting multiple lines of business through many distinct legal entities and across a range of geographies. While such complexity raises the the costs of bank resolution when organizations fail, the effect of complexity on BHCs' broader risk profiles is less well understood. Business, organizational, and geographic complexity can engender explicit trade-offs between the agency problems that increase risk and the diversification, liquidity management, and synergy improvements that reduce risk. The outcomes of such trade-offs may depend on bank governance arrangements. We test these conjectures using data on large U.S. BHCs for the 1996-2018 period. Organizational complexity and geographic scope tend to provide diversification gains and reduce idiosyncratic and liquidity risks while also increasing BHCs' exposure to systematic and systemic risks. Regulatory changes focused on organizational complexity have significantly reduced this type of complexity, leading to a decrease in systemic risk and an increase in liquidity risk among BHCs. While bank governance structures have, in some cases, significantly affected the buildup of BHC complexity, better governance arrangements have not moderated the effects of complexity on risk outcomes.