Multi-agent large language model (LLM) systems are increasingly adopted for complex language processing tasks that require communication and coordination among agents. However, these systems often suffer substantial overhead from repeated reprocessing of overlapping contexts across agents. In typical pipelines, once an agent receives a message from its predecessor, the full context-including prior turns-must be reprocessed from scratch, leading to inefficient processing. While key-value (KV) caching is an effective solution for avoiding redundant computation in single-agent settings where prefixes remain unchanged, it cannot be directly reused in multi-agent scenarios due to diverging prefixes introduced by agent-specific context extensions. We identify that the core challenge lies in the offset variance of KV-caches across agents. To address this, we propose KVCOMM, a training-free framework that enables efficient prefilling in multi-agent inference by reusing KV-caches and aligning cache offsets of overlapping contexts under diverse prefix contexts. KVCOMM estimates and adjusts KV-caches for shared content by referencing a pool of cached examples-termed anchors-that store observed cache deviations under varying prefixes. The anchor pool is maintained and updated online, allowing dynamic adaptation to distinct user requests and context structures. KVCOMM achieves over 70% reuse rate across diverse multi-agent workloads, including retrieval-augmented generation, math reasoning, and collaborative coding tasks, all without quality degradation. Particularly, when each fully-connected agent receives 1K input tokens with 512 prefix tokens and 512 output tokens under a five-agent setting, KVCOMM achieves up to 7.8x speedup compared to the standard prefill pipeline, reducing TTFT from ~430 ms to ~55 ms.