Integrating artificial intelligence (AI) in healthcare has sparked innovation but exposed vulnerabilities in regulatory oversight. Unregulated "shadow" AI systems, operating outside formal frameworks, pose risks such as algorithmic drift, bias, and disparities. The Comprehensive Algorithmic Oversight and Stewardship (CAOS) Framework addresses these challenges, combining risk assessments, data protection, and equity-focused methodologies to ensure responsible AI implementation. This framework offers a solution to bridge oversight gaps while supporting responsible healthcare innovation. CAOS functions as both a normative governance model and a practical system design, offering a scalable framework for ethical oversight, policy development, and operational implementation of AI systems in healthcare.