Medical decision-making often involves integrating knowledge from multiple clinical specialties, typically achieved through multidisciplinary teams. Inspired by this collaborative process, recent work has leveraged large language models (LLMs) in multi-agent collaboration frameworks to emulate expert teamwork. While these approaches improve reasoning through agent interaction, they are limited by static, pre-assigned roles, which hinder adaptability and dynamic knowledge integration. To address these limitations, we propose KAMAC, a Knowledge-driven Adaptive Multi-Agent Collaboration framework that enables LLM agents to dynamically form and expand expert teams based on the evolving diagnostic context. KAMAC begins with one or more expert agents and then conducts a knowledge-driven discussion to identify and fill knowledge gaps by recruiting additional specialists as needed. This supports flexible, scalable collaboration in complex clinical scenarios, with decisions finalized through reviewing updated agent comments. Experiments on two real-world medical benchmarks demonstrate that KAMAC significantly outperforms both single-agent and advanced multi-agent methods, particularly in complex clinical scenarios (i.e., cancer prognosis) requiring dynamic, cross-specialty expertise. Our code is publicly available at: https://github.com/XiaoXiao-Woo/KAMAC.