Quality enhancement methods have been widely integrated into visual communication pipelines to mitigate artifacts in compressed images. Ideally, these quality enhancement methods should perform robustly when applied to images that have already undergone prior enhancement during transmission. We refer to this scenario as multi-enhancement, which generalizes the well-known multi-generation scenario of image compression. Unfortunately, current quality enhancement methods suffer from severe degradation when applied in multi-enhancement. To address this challenge, we propose a novel adaptation method that transforms existing quality enhancement models into domain-consistent ones. Specifically, our method enhances a low-quality compressed image into a high-quality image within the natural domain during the first enhancement, and ensures that subsequent enhancements preserve this quality without further degradation. Extensive experiments validate the effectiveness of our method and show that various existing models can be successfully adapted to maintain both fidelity and perceptual quality in multi-enhancement scenarios.