Massively multilingual models, such as mBERT and XLM-R, can process text and provide representations for several languages relying on a shared set of parameters. Here, we discuss to what extent such systems can encode cross-lingual information in single network units. We present evidence in this respect for both syntactic phenomena, namely number agreement, and semantic properties, namely valence and arousal of words. We found that there is a significant overlap in the neurons that encode number agreement across five languages (English, German, French, Hebrew, Russian); common populations of neurons encoding for affective dimensions, on the other hand, were found for several languages. Such overlaps peak in the intermediate levels of the lexicon. This evidence suggests that symbol-like representations, at the levels of individual neurons, can naturally emerge in such muli-layer networks as a way to optimize learning.