Typically, you’d merge them together before loading into a database. “osmium” is one way of doing that, “osmosis” is another. One thing that a map server that I run does is splits a downloaded file into several pieces, translates each piece into a different language, and merges them all back together. The script that does all this (using osmosis) is here: https://github.com/SomeoneElseOSM/SomeoneElse-style/blob/master/update_render.sh .

There’s also documentation on osmosis and osmium in the OSM wiki and linked from it.