Saruman's Ring was no mere ornament.
He studied and worked long and hard to craft it, and knowing just what we do of Saruman's personality and pride, do you think he would boast to Gandalf of having crafted a useless ornament?
My opinion is that all of the Rings of power (which shall be capitalised from now on in this post) in some way worked on the hroa/fea and worked with sanwe. Anyone who doesn't know what these are - hroa/fea roughly corresponds to body/soul and sanwe is thought transference. Rather a lot about this can be found in a quite obscure essay by Tolkien that was published by an organisation who do work on his created languages. The Rings work on Men/mortals to break down the barrier of the hroa in particular - and in some way, the One may also have this effect on Sauron himself, who has been incarnated for far too long and is hence in a very vulnerable hroa.
Saruman will obviously have faced this problem in crafting his own Ring. Perhaps he managed to get over this in some way...and I have an idea how.
Another of my thoughts is that Light is held as divine in Arda, and we know that Saruman tried to 'break' the Light to see what it was made from. Thus, he becomes Saruman of Many Colours. It is quite possible that he sought this third way of Light breaking (as opposed to following a Light or Dark path) as some means of avoiding the risk Sauron took. Of course, if he did, then it ultimately failed as he was unbodied at Hobbiton.
It's also entirely possible for another One Ring to be made. A different one, yes, but very much possible, if one skilled enough had the know-how.
I'll come back to this because I want to watch some Plantagenets on telly, but meanwhile here's some of my old ramblings touching on this, which have some good quotes (I've nto just posted them because I can't be bothered
):
Rings of Power and Osanwe-kenta
The Mystery of Light