Meeting service-level objectives (SLOs) in Large Language Models (LLMs) serving is critical, but managing the high variability in load presents a significant challenge. Recent advancements in FP8 inference, backed by native hardware support, offer a potential solution: executing FP16 models by default, while switching to FP8 models during sudden load surges to achieve higher throughput at the cost of a slight quality degradation. Although this approach facilitates effective SLO management, it introduces additional memory overhead due to storing two versions of the same model. In response, this paper proposes NestedFP, an LLM serving technique that supports both FP16 and FP8 models in a memory-efficient manner by overlaying FP8 parameters onto FP16 parameters, allowing both models to share the same FP16 memory footprint. By leveraging a compact data format for the overlay and a specialized GEMM kernel optimized for this format, NestedFP ensures minimal degradation in both model quality and inference throughput across both FP8 and FP16 modes. NestedFP provides a flexible platform for dynamic, SLO-aware precision selection. The code is available at https://github.com/SNU-ARC/NestedFP.