The success of multilingual pre-trained models is underpinned by their ability to learn representations shared by multiple languages even in absence of any explicit supervision. However, it remains unclear how these models learn to generalise across languages. In this work, we conjecture that multilingual pre-trained models can derive language-universal abstractions about grammar. In particular, we investigate whether morphosyntactic information is encoded in the same subset of neurons in different languages. We conduct the first large-scale empirical study over 43 languages and 14 morphosyntactic categories with a state-of-the-art neuron-level probe. Our findings show that the cross-lingual overlap between neurons is significant, but its extent may vary across categories and depends on language proximity and pre-training data size.