Multi-task learning is to improve the performance of the model by transferring and exploiting common knowledge among tasks. Existing MTL works mainly focus on the scenario where label sets among multiple tasks (MTs) are usually the same, thus they can be utilized for learning across the tasks. While almost rare works explore the scenario where each task only has a small amount of training samples, and their label sets are just partially overlapped or even not. Learning such MTs is more challenging because of less correlation information available among these tasks. For this, we propose a framework to learn these tasks by jointly leveraging both abundant information from a learnt auxiliary big task with sufficiently many classes to cover those of all these tasks and the information shared among those partially-overlapped tasks. In our implementation of using the same neural network architecture of the learnt auxiliary task to learn individual tasks, the key idea is to utilize available label information to adaptively prune the hidden layer neurons of the auxiliary network to construct corresponding network for each task, while accompanying a joint learning across individual tasks. Our experimental results demonstrate its effectiveness in comparison with the state-of-the-art approaches.