Existing strategies for managing risks from advanced AI systems often focus on affecting what AI systems are developed and how they diffuse. However, this approach becomes less feasible as the number of developers of advanced AI grows, and impedes beneficial use-cases as well as harmful ones. In response, we urge a complementary approach: increasing societal adaptation to advanced AI, that is, reducing the expected negative impacts from a given level of diffusion of a given AI capability. We introduce a conceptual framework which helps identify adaptive interventions that avoid, defend against and remedy potentially harmful uses of AI systems, illustrated with examples in election manipulation, cyberterrorism, and loss of control to AI decision-makers. We discuss a three-step cycle that society can implement to adapt to AI. Increasing society's ability to implement this cycle builds its resilience to advanced AI. We conclude with concrete recommendations for governments, industry, and third-parties.