Accurate medical image segmentation is essential for effective diagnosis and treatment. Previously, PraNet-V1 was proposed to enhance polyp segmentation by introducing a reverse attention (RA) module that utilizes background information. However, PraNet-V1 struggles with multi-class segmentation tasks. To address this limitation, we propose PraNet-V2, which, compared to PraNet-V1, effectively performs a broader range of tasks including multi-class segmentation. At the core of PraNet-V2 is the Dual-Supervised Reverse Attention (DSRA) module, which incorporates explicit background supervision, independent background modeling, and semantically enriched attention fusion. Our PraNet-V2 framework demonstrates strong performance on four polyp segmentation datasets. Additionally, by integrating DSRA to iteratively enhance foreground segmentation results in three state-of-the-art semantic segmentation models, we achieve up to a 1.36% improvement in mean Dice score. Code is available at: https://github.com/ai4colonoscopy/PraNet-V2/tree/main/binary_seg/jittor.