Advances in artificial intelligence (AI) create game-changing opportunities and new risks for organizations. Increasing competition and emerging regulation pressure them to govern AI for strategic use. Portfolio management has been identified as a key mechanism. However, AI is different from technologies for which portfolio management has proven effective. How organizations design portfolio management to govern AI is not well understood. Therefore, we conceptualized key design decisions in AI portfolio management (AIPM) by developing a multi-layer taxonomy. We developed our taxonomy based on five exploratory case studies. We evaluated it through expert interviews and a practitioner intervention. Our taxonomy shows that many IT portfolio management characteristics also apply to AIPM. However, AI introduces complexities that require novel design decisions. Our taxonomy captures design knowledge that enables future causal / predictive theorizing on AIPM. Practitioners can use our taxonomy as a tool to establish and improve AIPM practices.