Multi-agent AI systems are the fastest-growing segment of enterprise AI, but most organizations deploying them are failing. Eight out of ten agentic AI projects never reach production, only 3 percent of companies have scaled agents across multiple departments, and Google DeepMind research shows that decentralized multi-agent systems amplify errors by 17.2x compared to single agents. Yet the organizations that get multi-agent right see extraordinary returns: 171 percent ROI, 700 percent accuracy improvements at PwC, and $20 million in savings at General Mills. In this third article of "Orchestrating the Hybrid Workforce," we examine the core design patterns that separate success from failure; sequential, parallel, hierarchical, router, evaluator, and event-driven; with specific guidance on when each pattern fits and when it breaks. We confront the complexity trap (single agents outperform multi-agent on 64 percent of benchmarked tasks), the hidden killers of context degradation and silent error propagation, the specialization-vs-generalization trade-off, and the four-level progression path from copilots to managed autonomy. The Orchestration Playbook covers pattern selection, the complexity maturity ladder, token economics (multi-agent systems consume 5-30x more tokens), and the five red flags that signal premature multi-agent complexity.