Beautiful room! While I have no problem at all with two or more rugs in the right setting, I'm not sure where you could add another. It looks too small by the fireplace area, and there is nothing to anchor a rug in the bare floor by the doorway. Leave it and let it shine. Gorgeous floor!

I can see the dilemma-tricky! Try breaking up the area where the sofa and arm chairs are and add some stools to that bar area. Then add a smaller area rug near the bar area with another arm chair and end table. I attached a sketch to give you an idea.