While the competence of LLMs to cope with agreement constraints has been widely tested in English, only a very limited number of works deals with morphologically rich(er) languages. In this work, we experiment with 25 mono- and multilingual LLMs, applying them to a collection of more than 5,000 test examples that cover the main agreement phenomena in three Romance languages (Italian, Portuguese, and Spanish) and one Slavic Language (Russian). We identify which of the agreement phenomena are most difficult for which models and challenge some common assumptions of what makes a good model. The test suites into which the test examples are organized are openly available and can be easily adapted to other agreement phenomena and other languages for further research.