Hi,
Thank you for your question. Tying the three neutral colors together may be best achieved in paint by choosing a "greige" color. These gray-beige colors are popular now, because they work often work well with gray and warm beige/browns. i can suggest some greige colors for you to sample.

Your other option is to choose a color that you like, but is different from the colors you're trying to coordinate, i.e. using a muted blue, green, or yellow as a wall color. In that case, adding accent decor in a print that represents the gray and browns together, would complete the look.

Here are some greige colors to consider for your walls:

Benjamin Moore Revere Pewter HC-172 http://www.myperfectcolor.com/en/color/102897_Benjamin-Moore-HC-172-Revere-Pewter

Match of Color Guild Estate Greige http://www.myperfectcolor.com/en/color/11719_Color-Guild-8682W-Estate-Greige

Match of Sherwin Williams Windsor Greige SW7528 http://www.myperfectcolor.com/en/color/286106_Sherwin-Williams-SW7528-Windsor-Greige

Benjamin Moore Skipping Stone CSP-155 http://www.myperfectcolor.com/en/color/378817_Benjamin-Moore-CSP-155-skipping-stone

Hope this is helpful,
Diana