Large language model (LLM) inference exhibits substantial variability across adaptation modes, context lengths, and request concurrency, creating challenges for maintaining high utilization, memory efficiency, and scalable performance on compute-in-memory (CIM) accelerators. This paper presents CHIPSMORE, a multi-mode and multi-request LLM inference accelerator that integrates compute-in-interconnect and CIM to support both base-mode and low-rank adaptation (LoRA) inference under diverse workloads. CHIPSMORE employs heterogeneous processing elements consisting of resistive RAM analog compute-in-memory (RRAM-ACIM) and static RAM digital compute-in-memory (SRAM-DCIM) interconnected through a programmable Inter-PE computational network (IPCN). A composable hierarchical key-value (KV) memory scheme dynamically allocates router scratchpad, SRAM-DCIM, and embedded DRAM (eDRAM) resources according to workload requirements, enabling scalable support for long-context and batched inference. Furthermore, a non-replicated multi-request execution pipeline exploits request-level parallelism without duplicating pretrained weights, while a state-aware resource reconfiguration mechanism selectively retains runtime states and power-gates inactive resources to improve energy efficiency. Evaluation using cycle-accurate hardware-software co-simulation demonstrates that CHIPSMORE effectively sustains high throughput across varying model sizes, context lengths, and batch sizes while maintaining favorable power scaling. Compared with Nvidia H100, CHIPSMORE achieves up to $2.38\times$ higher throughput and $27\times$ higher energy efficiency on Mistral-7B inference while eliminating weight replication for multi-request serving.

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