Annotation scarcity has become a major obstacle for training powerful deep-learning models for medical image segmentation, restricting their deployment in clinical scenarios. To address it, semi-supervised learning by exploiting abundant unlabeled data is highly desirable to boost the model training. However, most existing works still focus on limited medical tasks and underestimate the potential of learning across diverse tasks and multiple datasets. Therefore, in this paper, we introduce a \textbf{Ver}satile \textbf{Semi}-supervised framework (VerSemi) to point out a new perspective that integrates various tasks into a unified model with a broad label space, to exploit more unlabeled data for semi-supervised medical image segmentation. Specifically, we introduce a dynamic task-prompted design to segment various targets from different datasets. Next, this unified model is used to identify the foreground regions from all labeled data, to capture cross-dataset semantics. Particularly, we create a synthetic task with a cutmix strategy to augment foreground targets within the expanded label space. To effectively utilize unlabeled data, we introduce a consistency constraint. This involves aligning aggregated predictions from various tasks with those from the synthetic task, further guiding the model in accurately segmenting foreground regions during training. We evaluated our VerSemi model on four public benchmarking datasets. Extensive experiments demonstrated that VerSemi can consistently outperform the second-best method by a large margin (e.g., an average 2.69\% Dice gain on four datasets), setting new SOTA performance for semi-supervised medical image segmentation. The code will be released.