Large language model (LLM) serving is now limited by the key-value (KV) cache. During decode, each new token rereads prior KV state, so attention becomes a bandwidth- and capacity-heavy memory task. HBM-PIM helps by moving attention closer to memory, but current stack organizations still waste resources. In practice, only hot KV blocks benefit from near-memory compute. Weights, activations, and cold KV mainly need dense storage and GPU-visible bandwidth. A uniform HBM-PIM stack makes all layers pay for PIM logic, while a dedicated-PIM design such as AttAcc recovers capacity but shrinks the HBM bandwidth left for GPU-side work. We propose TokenStack, a vertically heterogeneous HBM-PIM architecture for KV-centric LLM serving that leverages HBM4's logic-die substrate. TokenStack separates each stack into dense capacity layers and PIM-enabled compute layers, then uses the logic base die as a stack-local control point that manages cross-layer movement without host-side overhead. The base-die controller handles cross-layer DMA, layered address translation, attention-side gather/broadcast coordination, and inline quantization during migration. On top of this hardware, TokenStack uses topology-aware KV placement, workload-aware eviction, and bounded replication to keep hot KV near PIM compute while moving colder state to dense layers. Using production-derived traces across four models, completed multi-QPS runs show that TokenStack increases geometric-mean token throughput by 1.62x and SLO-compliant serving capacity by 1.70x over AttAcc, and reduces per-token energy by 30-47%.

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