Let's call every language a skill, and let's also make a universal language called Portal Pidgin. We'll assume it's so incredibly simple that almost anyone can learn to speak it passably after a couple of weeks immersion. PCs are fully fluent, they've been through Troika, or lived there, or just dealt with those ambiguously foreign traders everyone seems to have been visited by.
Portal Pidgin is almost a Unified Theory of Language, the roiling sweaty pile of interdimensional culture at the centre of the universe has solved communication. Knowledge of it grants a deep understanding of language, a unique vantage point from which to approach new ways of speech. People native to it have little trouble picking up the basics of any new language met.
Every time a PC meets a new language they may test their Skill to fumble through it. If they fail, they get no where, if they pass they manage to communicate basic desires and get an advancement tick in that particular language.
However unlike standard skills, advancement is not a matter of rolling higher than your current skill. Instead each language has an in built difficulty. If you don't have one in mind, just roll a d6. That is how difficult that language is to learn, and with each advancement you must roll equal to or greater than that number.
When talking to some foreign sorts, roll against you Skill. If you pass, you can chat to them roughly, if you fail you get lost.
If you roll a critical on your language check you instantly take an advancement test.
If you fumble your test you must roll below:
1-3 Your audience has become tired with your hooting and pointing and refuse to participate any longer. This goes for the whole party.
4 You have offended them somehow. They respond appropriately, be that with indignation or violence.
5 They have got the wrong end of the stick, thinking you are trying to say the exact opposite of what you meant. This could cause issues while protesting innocence or complimenting someone.
6 You have accidentally been obscene, insulting religion or state. Their response will depend on the context, but assume the guards are being called right now.
Once a PC has 6 in a language they are assumed to be completely fluent to all but its most arcane usages.
In a long campaign the PCs will develop cultural scars. They'll look at the list of languages they can stumble through and see the trail they took up to this point.