Deep learning empowers the mainstream medical image segmentation methods. Nevertheless current deep segmentation approaches are not capable of efficiently and effectively adapting and updating the trained models when new incremental segmentation classes (along with new training datasets or not) are required to be added. In real clinical environment, it can be preferred that segmentation models could be dynamically extended to segment new organs/tumors without the (re-)access to previous training datasets due to obstacles of patient privacy and data storage. This process can be viewed as a continual semantic segmentation (CSS) problem, being understudied for multi-organ segmentation. In this work, we propose a new architectural CSS learning framework to learn a single deep segmentation model for segmenting a total of 143 whole-body organs. Using the encoder/decoder network structure, we demonstrate that a continually-trained then frozen encoder coupled with incrementally-added decoders can extract and preserve sufficiently representative image features for new classes to be subsequently and validly segmented. To maintain a single network model complexity, we trim each decoder progressively using neural architecture search and teacher-student based knowledge distillation. To incorporate with both healthy and pathological organs appearing in different datasets, a novel anomaly-aware and confidence learning module is proposed to merge the overlapped organ predictions, originated from different decoders. Trained and validated on 3D CT scans of 2500+ patients from four datasets, our single network can segment total 143 whole-body organs with very high accuracy, closely reaching the upper bound performance level by training four separate segmentation models (i.e., one model per dataset/task).