We already added for the next update the Nine Rings of the Men, more powerful than the dwarvish ones, but less than the elvish.
I'll probably make some events to gain some "bad" traits like depressed for holders of any ring of power, yes (without the elven ones)!
For the ability to make new Rings of Powers, i don't think so. Celebrimbor was able to, but he wasn't like any other elves, he was the descendant of Feanor, the greatest of all the elves. It's only because he was like Feanor (with less powers) that he was able to make the Three Rings, and because Annatar/Sauron teached him how to do. Sauron won't teach anyone else now, and even Saruman tried to make one, and failed. I don't think that the Noldor jewelsmiths of Third Age are able to make stuff like this.
The elves, before the coming of Annatar, were able to craft some Lesser Rings, so maybe we'll allow this possibility. But a Ring of Power, i don't think so