Sparse expert activation reduces MoE models' computation, yet expert weights can exceed limited device memory. Offloading makes inference feasible on a compact AI appliance but exposes host-to-device transfers to the inference path. We present MoE-CORE, a system that coordinates expert offloading and residency for memory-constrained MoE inference. It stages complete expert layers in alternating buffers during prefill. During decode, it combines nonuniform layer-wise cache capacity, domain-informed initialization, routing-history-aware replacement, and cross-layer prefetching. The main configuration executes router-selected experts exactly; an optional score-based substitution path handles eligible low-score misses. The main comparison uses 1K- and 128-token output caps for MoE-CORE and vLLM Prefetch, respectively. Across five workloads per model, MoE-CORE records a mean time per output token (TPOT) of 38.0-44.8 ms versus 1268.9-1269.1 ms for the evaluated vLLM Prefetch configuration on DeepSeek-V4-Flash-W4A8; the corresponding values on GLM-5.2-W4A8C8 are 206.6-220.5 and 5941.5-5941.8 ms. Under an 84-GB NPU-memory cap, the best measured DeepSeek GSM8K configuration achieves a TPOT of 21.5 ms with approximate expert substitution and multi-token prediction (MTP) at depth 2. These results support coordinated expert residency and transfer scheduling under a device-memory constraint. The code is here.

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