Multi-agent large language model systems offer a promising paradigm for multidisciplinary medical decision support by integrating heterogeneous expert perspectives. However, existing frameworks often rely on loosely structured interactions, where disagreement is insufficiently diagnosed and discussion may collapse into superficial consensus or parallel opinion aggregation. We propose Structured Adaptive Multi-disciplinary Collaboration (SAMAC), a structured and strategy-aware multi-agent framework for adaptive MDT-style medical reasoning. SAMAC introduces Structured Deliberation to detect opinion disagreement and majority not confident, along with a Consensus Purification mechanism that transforms disagreement into constructive and collaborative refinement. When disagreement arises, SAMAC adaptively selects between Self-refinement and Counter-questioning to enable evidence-grounded negotiation. Experiments on three medical datasets—RADCURE, HANCOCK, and OSCCPI—show that SAMAC consistently improves overall performance and collaborative gains over existing multi-agent baselines. In particular, SAMAC improves the Average Score by 4.29 points on the RADCURE dataset and achieves higher Relative Self-Correction Scores (RSS), indicating more effective resolution of disagreement and stable collective decisions. These results highlight the importance of controlled and diverse interaction dynamics in multi-agent medical reasoning. Code will be released upon publication.