Multi-frame video enhancement tasks aim to improve the spatial and temporal resolution and quality of video sequences by leveraging temporal information from multiple frames, which are widely used in streaming video processing, surveillance, and generation. Although numerous Transformer-based enhancement methods have achieved impressive performance, their computational and memory demands hinder deployment on edge devices. Quantization offers a practical solution by reducing the bit-width of weights and activations to improve efficiency. However, directly applying existing quantization methods to video enhancement tasks often leads to significant performance degradation and loss of fine details. This stems from two limitations: (a) inability to allocate varying representational capacity across frames, which results in suboptimal dynamic range adaptation; (b) over-reliance on full-precision teachers, which limits the learning of low-bit student models. To tackle these challenges, we propose a novel quantization method for video enhancement: Progressive Multi-Frame Quantization for Video Enhancement (PMQ-VE). This framework features a coarse-to-fine two-stage process: Backtracking-based Multi-Frame Quantization (BMFQ) and Progressive Multi-Teacher Distillation (PMTD). BMFQ utilizes a percentile-based initialization and iterative search with pruning and backtracking for robust clipping bounds. PMTD employs a progressive distillation strategy with both full-precision and multiple high-bit (INT) teachers to enhance low-bit models' capacity and quality. Extensive experiments demonstrate that our method outperforms existing approaches, achieving state-of-the-art performance across multiple tasks and benchmarks.The code will be made publicly available at: https://github.com/xiaoBIGfeng/PMQ-VE.