We present edition 2.0 of the PARSEME multilingual corpus annotated for multiword expressions (MWEs), resulting from efforts of the PARSEME community towards universality-driven modeling of idiomaticity. With respect to previous editions, we extend the annotation scope to all syntactic MWE categories: verbal, nominal, adjectival, adverbial and functional. We cover 17 languages, of which 7 are new. The annotation process is based on cross-lingually unified guidelines, phrased as decision diagrams over linguistic tests, and a typology of 18 MWE categories. The corpus contains almost 5 million tokens, over 250,000 sentences and 140,000 MWE annotations. The applicability of the corpus is tested in baseline experiments with a prompt-based MWE identification system. Results show that generic large language models do not encode sufficient knowledge to solve the MWE identification task.