Enterprise AI systems increasingly deploy multiple intelligent agents across mission-critical workflows that must satisfy hard policy constraints, bounded risk exposure, and comprehensive auditability (SOX, HIPAA, GDPR). Existing coordination methods - cooperative MARL, consensus protocols, and centralized planners - optimize expected reward while treating constraints implicitly. This paper introduces CAMCO (Constraint-Aware Multi-Agent Cognitive Orchestration), a runtime coordination layer that models multi-agent decision-making as a constrained optimization problem. CAMCO integrates three mechanisms: (i) a constraint projection engine enforcing policy-feasible actions via convex projection, (ii) adaptive risk-weighted Lagrangian utility shaping, and (iii) an iterative negotiation protocol with provably bounded convergence. Unlike training-time constrained RL, CAMCO operates as deployment-time middleware compatible with any agent architecture, with policy predicates designed for direct integration with production engines such as OPA. Evaluation across three enterprise scenarios - including comparison against a constrained Lagrangian MARL baseline - demonstrates zero policy violations, risk exposure below threshold (mean ratio 0.71), 92-97% utility retention, and mean convergence in 2.4 iterations.

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