It is possible but it is definitely hard. Since all languages have different grammar constructions, vocabularies, pronunciation, accent, etc. If you are a little kid who's still learning to speak it may be easy for you since children were proven to learn languages easier because they haven't been exposed to one language for too long yet but for adults like us we have to cram to learn even just one language. Learning a language is exposing yourself to it no matter how many languages is that so if you really want to do it then start reading a story translated to three languages. I hope this helps.

I would personally recommend that you only actively learn two at the same time. You can still maintain the other languages you have already learnt by reading the occasional news article or something. If you learn more two at the same time, you run the risk of spreading yourself too thin.

In my opinion it is possible. I'm learning four languages at the same time and it works! :) I think it depends on which languages you learn as some need more time (Chinese for example). But if they have a similar grammar, it is easy. I learn my languages at school, so I have a schedule which tells me when to learn. You can try that, as well :) One hour of English, one hour of French... Or which language you learn :D

Thanks to all answers. ^^