The recent advances in LLMs bring a strong demand for efficient system support to improve overall serving efficiency. As LLM inference scales towards multiple GPUs and even multiple compute nodes, various coordination patterns, such as prefill-decode disaggregation and context migration, arise in serving systems. Most inference services today expose a coarse-grained request-level API with a pre-configured coordination strategy, limiting the ability to customize and dynamically reconfigure the coordination. In this paper, we propose MicroServe, a multi-level architecture for structuring and programming LLM inference services. MicroServe introduces simple yet effective APIs to support fine-grained sub-request level actions. A programmable router transforms user requests into sub-request calls, enabling the dynamic reconfiguration of serving patterns. To support diverse execution patterns, we develop a unified KV cache interface that handles various KV compute, transfer, and reuse scenarios. Our evaluation shows that MicroServe can be reconfigured to support multiple disaggregation orchestration strategies in a few lines of Python code while maintaining state-of-the-art performance for LLM inference tasks. Additionally, it allows us to explore new strategy variants that reduce up to 47% of job completion time compared to the existing strategies.