Sparse attention limits the keys used by each query, but finding those keys can still require a full-prefix scan at every layer. We introduce $MLIPS:$ $Multi$-$Layer$ $Indexer$ $Pool$ $Sharing$, a training-free method that shares candidate search while retaining each consumer's own scoring and selection. A producer publishes a top-$M$ pool larger than the attention budget $K$; subsequent layers select their own top-$K$ from that pool. Measurements across three sparse-attention model families show substantially higher coverage from broad pools than overlap between final selections. We implement layerwise sharing, persistent decode reuse, and a coarse producer in vLLM for DeepSeek-V4-Flash. Across four long-context suites, three consumer layers per producer give $1.14$-$1.40\times$ speedups and $14.8$-$27.4\%$ lower GPU energy, with observed accuracy changes of $-1.49$ to $+0.29$ percentage points in single runs. More extensive sharing exposes task-dependent quality losses. Sampled prefill traces also reveal recurring selected KV positions across query groups and layers. We characterize this shared working-set structure and use it to motivate Top-$G$, an exploratory bounded pool construction for prefill. Its deployment, task accuracy, and serving benefits remain open.

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