Nuclei Segmentation and Classification are crucial in computational pathology, but they encounter various challenges. These include identifying subtle differences between nucleus classes, managing nuclei morphology diversity, and high-class imbalance. This work proposes a modular three-stage segmentation architecture to simplify the complex segmentation task and tackle each challenge individually. The first stage uses a detection network to accurately localize each nucleus and obtain its bounding box, creating a set of single-nucleus images. The bounding boxes are used to extract the nucleus segmentation masks and then go through a context-aware adder for additional context on both axes. Then, we train a multi-class semantic segmentation network to segment each nucleus independently. Finally, the segmented nuclei undergo a Class Consistency Check and Correction ( \(C^{4}\) ) block before being put together to obtain the final mask for the full image. As our proposed architecture focuses on modularity, we propose two variants of Multi-stage Detection-Segmentation Network (MDSN) focusing on performance (MDSN-c) and efficiency (MDSN-s). MDSN-c outperforms HoVer-Net model and Mask-RCNN101 by 0.7 and 21.7% on dice score, respectively. MDSN-s achieves a 19.8% dice score improvement over Mask-RCNN101 and performs comparably to HoVer-Net with 69.8% less parameters. The code is available at https://github.com/HussamAzzuni/MDSN .