Grosso modo is a phrase of Latin origin, meaning "approximately". The phrase has been adopted in many languages (like English, French, Dutch, etc), as the referred link testifies. The interesting thing is this: the phrase is also native Italian.
According to this unscientific blog entry, it has been used at least since the XIVth century. That is quite late Latin and a time where romances languages (like Italian) were already developing fast.
The question is then, are we sure the popularisation of such phrase emanate from the Latin (as it seems to be believed) rather than from the Italian? I would imagine the answer hinges on an analysis of the corpus of where such phrase is adopted, for instance, scientific (Latin) versus literary (Italian) work. I couldn't know how to perform such analysis, let alone if it is the right approach. Any ideas?