It can be done, and so is realistic in that fashion.
However, few people actually learn that many because life gets in the way.
How competent you want to be in each language is also a factor, but nevertheless full competency in 20 languages over a life time is possible.
Keep in mind, though, that you have to use languages frequently (daily is best), or you will lose some competency (at least until you start using it regularly again). If you intend to maintain a specific competency level, you have to practice each language regularly. If you do that, you will have less time to devote to the next new language, with every language you accumulate.
Your goal is possible, but by no means easy. It will require discipline, time, and effort sustained for decades (really the rest of your life. If you learn all 20 say within 10 years, you still have to practice them if your goal is to remain competent).
Of course, it's a lot easier if your goals are less ambitious.
four foreign languages; taught one of them. Started at 15. I am now 48. I practice all of them daily. I have varying degrees of competency depending on the language (by design). also studied linguistics and phonology and how to teach languages. native English speaker