My school, when I was in the studying age (talking mid-high-start of college...it was an 8 year grammar school), always required two or more languages at the same time. True, most schools in my country provided only European ones and not something as different as East Asian languages, but you still had to pick English, German, Russian, French, Italian, Hungarian...some combination of two.

So yeah; you definitely can. Especially if you're young and have most of your time possibly dedicated to study.

I am a self-learner now, many years later, and I tried doing Japanese alongside with Korean and Arabic, but I had to drop the Korean (and most of Arabic) as way too much at the moment. I do have a hazy plan to eventually pick it back up when I'm deeper and more sure in Japanese..