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.