As much as we all love stained wood, off white (Dove White?) would greatly improve the space. I cannot tell if the background color is a plum, but if so, that wold be my suggestion. It does not have to be a solid but could be a fine pattern with that plum and a lighter dot or design, just not as big as the pattern of the carpet.

The background of the center hall carpet is brown tones.

I wouldn't go brown on the walls it would be too dark, take a look at this colour




I copied that :)
Similar colors are Sand Dollar 6099 and Portabello 6102 by Sherwin-Williams.

really like the rug.