Accurate segmentation of the primary gross tumor volumes and metastatic lymph nodes in head and neck cancer is crucial for radiotherapy but remains challenging due to high interobserver variability, highlighting a need for an effective auto-segmentation tool. Tumor delineation is used throughout radiotherapy for treatment planning, initially for pre-radiotherapy (pre-RT) MRI scans followed-up by mid-radiotherapy (mid-RT) during the treatment. For the pre-RT task, we propose a dual-stage 3D UNet approach using cascaded neural networks for progressive accuracy refinement. The first-stage models produce an initial binary segmentation, which is then refined with an ensemble of second-stage models for a multiclass segmentation. In Head and Neck Tumor Segmentation for MR-Guided Applications (HNTS-MRG) 2024 Task 1, we utilize a dataset consisting of pre-RT and mid-RT T2-weighted MRI scans. The method is trained using 5-fold cross-validation and evaluated as an ensemble of five coarse models and ten refinement models. Our approach (team FinoxyAI) achieves a mean aggregated Dice similarity coefficient of 0.737 on the test set. Moreover, with this metric, our dual-stage approach highlights consistent improvement in segmentation performance across all folds compared to a single-stage segmentation method.