Short answer is yes, the [R] mediation package can do this.

What I also see sometimes is that researchers drop the top and bottom X % of their observations to reduce the influence of extreme cases. But I'm unsure whether I agree with it, it's quite arbitrary isn't it?

Thanks for your suggestion. Now, this code is running for over half an hour now, is this because of the size of my data or is there a little mistake in the code? I already tried to look up some stuff about the code but I'm not that skilled with the STATA Syntax yet.