Medical text simplification is crucial for making complex biomedical literature more accessible to non-experts. Traditional methods struggle with the specialized terms and jargon of medical texts, lacking the flexibility to adapt the simplification process dynamically. In contrast, recent advancements in large language models (LLMs) present unique opportunities by offering enhanced control over text simplification through iterative refinement and collaboration between specialized agents. In this work, we introduce the Society of Medical Simplifiers, a novel LLM-based framework inspired by the "Society of Mind" (SOM) philosophy. Our approach leverages the strengths of LLMs by assigning five distinct roles, i.e., Layperson, Simplifier, Medical Expert, Language Clarifier, and Redundancy Checker, organized into interaction loops. This structure allows the agents to progressively improve text simplification while maintaining the complexity and accuracy of the original content. Evaluations on the Cochrane text simplification dataset demonstrate that our framework is on par with or outperforms state-of-the-art methods, achieving superior readability and content preservation through controlled simplification processes.