The typical process for developing LLMs involves pre-training a general foundation model on massive data, followed by fine-tuning on task-specific data to create specialized experts. Serving these experts poses challenges, as loading all experts onto devices is impractical, and frequent switching between experts in response to user requests incurs substantial I/O costs, increasing latency and expenses. Previous approaches decompose expert weights into pre-trained model weights and residual delta weights, then quantize the delta weights to reduce model size. However, these methods often lead to significant quantization errors at extremely low bitwidths and assume the appropriate model for a user request is known in advance, which is not practical. To address these issues, we introduce ME-Switch, a memory-efficient expert switching framework for LLM serving. ME-Switch uses mixed-precision quantization, selectively quantizing non-salient input channels of delta weights to extremely low bits while keeping salient ones intact, significantly reducing storage demands while maintaining performance. Additionally, we develop a routing method that efficiently directs user queries to the most suitable expert by transforming the model selection problem into a domain classification problem. Extensive experiments show ME-Switch's promising memory efficiency and routing performance. For example, when serving three models from the Mistral-7B family, ME-Switch reduces model size by 1.74x while maintaining nearly lossless performance on instruction, mathematical reasoning, and code generation tasks. Furthermore, ME-Switch can efficiently serve 16 models from the Mistral-7B family on a single NVIDIA A100 GPU.