Optical absorption and scattering result in quality degradation of underwater images, which hampers the performance of underwater vision tasks. In practice, a well-posed underwater image recovery requires a combination of scene specificity and adaptability. To this end, this paper breaks down the overall recovery process into in-situ enhancement and data-driven correction modules, and proposes a Multi-stage Underwater Image Enhancement (MUIE) method to cascade the modules. In the in-situ enhancement module, a channel compensation with scene-relevant supervision is designed to address different degrees of unbalanced attenuation, and then the duality-based computation inverts the result of running a enhancement on inverted intensities to recover the degraded textures. In response to different scenarios, a data-driven correction, encoding corrected color-constancy information under data supervision, is performed to correct the improper color appearance of in-situ enhanced results. Further, under the collaboration between scene and data information, the recovery of MUIE avoids ill-posed response and reduces the prior dependence of specific scenes, resulting in a robust performance in different underwater scenes. Recovery comparison results confirm that the recovery of MUIE shows the superiority of scene clarity, realistic color appearance and evaluation scores. With the recovery of MUIE, the Underwater Image Quality Measurement (UIQM) scores of recovery-challenging images in the UIEB dataset were improved from 1.59 to 3.92.