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Operating room (OR) turnover represents a critical bottleneck in surgical workflows, where delays in transitioning between procedures can cascade into inefficiencies, increased costs, and compromised patient care. This conceptual manuscript introduces a blueprint for multi-agent coordination grounded in constraint-based optimization to streamline OR turnover processes. Drawing from clinical AI architectures and healthcare analytics infrastructures, we propose the constraint-adaptive multi-agent turnover orchestrator (CAMATO). This theoretical framework integrates autonomous agents for real-time task allocation, resource synchronization, and procedural handoffs. CAMATO leverages interoperability frameworks and decision support pipelines to model turnover as a constrained optimization problem, incorporating variables such as staff availability, equipment sterilization cycles, and environmental constraints. The architecture emphasizes governance mechanisms to monitor agent interactions and mitigate coordination failures, ensuring alignment with electronic health record (EHR) intelligence ecosystems. Through interpretive formulas, we conceptualize risk propagation in agent networks, decision confidence under uncertainty, and resource allocation dynamics. This blueprint highlights the potential for enhanced clinical workflow integration without empirical validation, focusing on theoretical implications for scalable, resilient OR management. By synthesizing recent literature on AI-driven healthcare systems, we outline pathways for future architectural refinements in high-stakes clinical environments.