Liver fibrosis poses a substantial challenge in clinical practice, emphasizing the necessity for precise liver segmentation and accurate disease staging. Based on the CARE Liver 2025 Track 4 Challenge, this study introduces a multi-task deep learning framework developed for liver segmentation (LiSeg) and liver fibrosis staging (LiFS) using multiparametric MRI. The LiSeg phase addresses the challenge of limited annotated images and the complexities of multi-parametric MRI data by employing a semi-supervised learning model that integrates image segmentation and registration. By leveraging both labeled and unlabeled data, the model overcomes the difficulties introduced by domain shifts and variations across modalities. In the LiFS phase, we employed a patchbased method which allows the visualization of liver fibrosis stages based on the classification outputs. Our approach effectively handles multimodality imaging data, limited labels, and domain shifts. The proposed method has been tested by the challenge organizer on an independent test set that includes in-distribution (ID) and out-of-distribution (OOD) cases using three-channel MRIs (T1, T2, DWI) and seven-channel MRIs (T1, T2, DWI, GED1-GED4). The code is freely available. Github link: https://github.com/mileywang3061/Care-Liver