I don't think you need to ask permission in as much as you need to at least tell your sensei that you're going to take another martial art. Some instructors, myself included, aren't real hot on students doing that. It takes many. MANY years to master just one martial art. I've been doing the same one for over 30 years now and still haven't got it down yet, nor do I expect I ever will. Training in two or more at the same time dosen't do justice to either of them. Find one that suits you best and dive into it full out. If it's not what you expect out of an art, then quit and move on until you do find what you desire.
I don't think you need to ask permission in as much as you need to at least tell your sensei that you're going to take another martial art. Some instructors, myself included, aren't real hot on students doing that. It takes many. MANY years to master just one martial art. I've been doing the same one for over 30 years now and still haven't got it down yet, nor do I expect I ever will. Training in two or more at the same time dosen't do justice to either of them. Find one that suits you best and dive into it full out. If it's not what you expect out of an art, then quit and move on until you do find what you desire.