Learning more than one language at once

So, I'm a student of German.
Basically I am at the point where I do not have a huge vocabulary, but I have vast knowledge of German grammar so understanding the language is just a matter of looking up unknown words.

Anyway, recently I've started studying Dutch.

My friend rebelled against me, saying that I'm going to fuck my shit all up.

Why? It's not like I mix up the two languages in my head.

Do you study more than one language at once? If not, why?

I'm trying to learn Japanese and Turkish at the same time.

Don't ask.

As completely different as the languages are though, it looks like they seem to conjugate verbs in the same way...