AbstractThis paper describes the system of our team SJTU for our participation in the CoNLL 2019 Shared Task: Cross-Framework Meaning Representation Parsing. The goal of the task is to advance data-driven parsing into graph-structured representations of sentence meaning. This task includes five meaning representation frameworks: DM, PSD, EDS, UCCA, and AMR. These frameworks have different properties and structures. To tackle all the frameworks in one model, it is needed to find out the commonality of them. In our work, we define a set of the transition actions to once-for-all tackle all the frameworks and train a transition-based model to parse the meaning representation. The adopted multi-task model also can allow learning for one framework to benefit the others. In the final official evaluation of the shared task, our system achieves 42% F1 unified MRP metric score.