I think there's not really a limitation but more of how many will you retain after a few weeks/months/years. In a way, there's also a technique on how to learn languages fast which will help you if your memory of a certain language was stored in your brain.
According to this guide (the reference is below), here are the best ways to learn languages fast:
1) It’s necessary to listen at a natural speech rate when learning a new language;
2) Start learning a new language by focusing on speech rather than text;
3) The distinction between studying and learning a language;
4) Language learning is possible through comprehensible input, which is an unconscious process.
5) The spaced repetition strategy can help you recall information.
6) Other basic approaches for how to learn foreign languages fast and effectively like taking live lessons or self-study programs that prompt you to speak.
Which one of these tips do you think you can relate or agree with? I think I'm more of number 2 and 4.
Here's the link to the whole article for the source: https://www.youtube.com/watch?v=t2is7Vi7WXw (Their documentary video)