We present PERIN, a novel permutation-invariant approach to sentence-to-graph semantic parsing. PERIN is a versatile, cross-framework and language independent architecture for universal modeling of semantic structures. Our system participated in the CoNLL 2020 shared task, Cross-Framework Meaning Representation Parsing (MRP 2020), where it was evaluated on five different frameworks (AMR, DRG, EDS, PTG and UCCA) across four languages. PERIN was one of the winners of the shared task. The source code and pretrained models are available at https://github.com/ufal/perin.