In this paper, we describe our participating systems in the shared task on Cross- Framework Meaning Representation Parsing (MRP) at the 2019 Conference for Computational Language Learning (CoNLL). The task includes five frameworks for graph-based meaning representations, i.e., DM, PSD, EDS, UCCA, and AMR. One common characteristic of our systems is that we employ graph-based methods instead of transition-based methods when predicting edges between nodes. For SDP, we jointly perform edge prediction, frame tagging, and POS tagging via multi-task learning (MTL). For UCCA, we also jointly model a constituent tree parsing and a remote edge recovery task. For both EDS and AMR, we produce nodes first and edges second in a pipeline fashion. External resources like BERT are found helpful for all frameworks except AMR. Our final submission ranks the third on the overall MRP evaluation metric, the first on EDS and the second on UCCA.