Well, deep red works well with a chocolate brown. No other color is going to go with the red unless you choose a shade like white or beige. Other than that, I recommend using a dark chocolate brown. It will compliment your room for sure because both deep red and brown go well together and that combination has been used for ages. I hope this helps.

Dark blue would suit the adjoining bathroom. Red and blue combination's are quite attractive and are used at many places. Even with clothing, such a combination sells better than other combination's of red. You can even try the combination on a piece of paper using red and blue colored sketch pens to notice the difference yourself.

For a stark contrast, try a cream color, for a not so stark contrast, go grey.