Modern LLM serving systems increasingly host agentic workloads, whose sessions issue tens of model invocations interleaved with tool calls, accumulating KV cache that can be reused across steps. As requests' total KV cache size easily exceeds GPU HBM capacity, researchers offload them to CPU DRAM. However, tool-call durations span orders of magnitude, and the cost of transferring KV cache between tiers makes it impractical to re-place entries on every call. We observe that agentic programs exhibit a two-phase structure: busy phases of rapid short tool calls and idle phases dominated by long-running calls. Current eviction policies such as LRU fail to capture this property. A binary busy/idle label also falls short because the ratio of busy to idle programs may not match the hardware's GPU-to-CPU capacity ratio. When it does not, one tier sits underutilized while the other is oversubscribed, wasting memory or forcing unnecessary evictions. We present MORI, an agent serving system that solves the above problem. Our key insight is that idleness is a continuous, relative spectrum. MORI ranks all active programs by idleness, assigns the busiest to GPU HBM and the most idle to CPU DRAM, dynamically shifts the partition boundary to match hardware capacity, and enforces admission control at each memory tier. Evaluated on real coding agent workloads collected from Claude Code across four GPU and model pairs, MORI delivers 20--71% higher throughput and 18--43% lower TTFT than the best baseline with offloading.

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