Multi-agent LLM systems have become the dominant production workload, but the serving stack was not built for them. The agent framework above knows agent identities, role, schemas, and dispatch structure but never sees an engine-level event; the serving engine below sees every event but knows nothing about agents. A surprising number of cross-cutting policies depend on both: prefix caching, batch shaping, speculative execution, fairness, tool-result memoization, safety enforcement, and more. Each lives in the seam between the two layers and is currently solved by a one-off patch into one neighbor or the other. We argue this seam is best addressed by an architectural change rather than point fixes: insert a third tier, an agent runtime layer, between the framework and the engine, exposing four primitives (observe, score, predict, act) into which any agent-aware policy plugs, with agent identity as the shared coordinate. We map nine concrete policies onto the layer and validate the abstraction in depth on the one with the largest immediate serving-cost lever: KV caching across sessions, instantiated as CacheSage, which learns the per-workload agent transition matrix online and uses it for survival-based eviction and between-step prefetch. Preliminary results on five real multi-agent workloads show +13 to +37 pp cache hit-rate lift, 12% to 29% lower mean TTFT, and 6% to 14% higher throughput over an unmodified serving stack.