Then there's the question...should the furniture sit entirely on, or entirely off, or somewhere in between. Let me be honest and say I don't have a "professional" opinion, but would say that it depends on the thickness of the rug. I'd say that half on, half off, would be less desirable.
Can I put a rug on top of carpet? Hmmm, that also really depends on the weight/thickness of the carpet and the thickness of the rug. A thin carpet can host a shaggy rug much easier than the opposite!
I am thankful for design tools when making decisions like this. It's so nice to be able to pop these ideas into 3D. It also helps to consider the drapery, pillows, coffee table books...tying the space together helps to see that the rug does not have to say it all. "All of the space" says it all.
Now go ahead, and Get Ruggy With It.
P.S. I think West Elm has a nice area rug collection. (I am not getting any perks for recommending this.)