So I'm currently leveling my classes, and I have all of them unlocked at various levels. Today, I was informed I could not change my rings because I have no more room in the armory chest.
I think this is a bit of an oversight for Heavensward, considering that you have to use two of them and that you are going to have many classes at different levels as you level them up. Especially once we get into Eso gear and its a different set for every class.
I suggest, at the very least, add just one more row in order to incorperate the number of rings you are going to need if you intend to work on multiple classes.