Sequential pattern mining is used to find frequent data sequences over time. When sequential patterns are generated, the newly arriving patterns may not be identified as frequent sequential patterns due to the existence of old data and sequences. Progressive sequential pattern mining aims to find the most up-to-date sequential patterns given that obsolete items will be deleted from the sequences. When sequences come with multiple data streams, it is difficult to maintain and update the current sequential patterns. Even worse, when we consider the sequences across multiple streams, previous methods cannot efficiently compute the frequent sequential patterns. In this work, we propose an efficient algorithm PSP-AMS to address this problem. PSP-AMS uses a novel data structure PSP-MS-tree to insert new items, update current items, and delete obsolete items. By maintaining a PSP-MS-tree, PSP-AMS efficiently finds the frequent sequential patterns across multiple streams. The experimental results show that PSP-AMS significantly outperforms previous algorithms for mining of progressive sequential patterns across multiple streams on synthetic data as well as real data.