First of all, there was plenty of international trade going on, so a surprising number of people probably spoke multiple languages. Merchants in particular, as well as bureaucrats responsible for customs duties and tax collection probably spoke multiple languages.

Secondly, most rulers probably had multiple scribes who were each literate in multiple languages as well.

There were also probably common languages as well, most likely originated in the big empires. So, a lot of people probably spoke Greek, Latin, Egyptian, or Persian to some extent.