Private Dining Sought in Fairfax area

I am planning to host a private dining event for 18-20 people in Jan-Feb. I want an upscale restaurant, a private room, and an a la carte menu. For example, Colvin Run Tavern would be perfect but the room holds a max of 12. Maestro is too pricey. 2941 requires a use of a limited banquet menu. I prefer Fairfax area (not Arlington or ALexandria). Any ideas? Thanks in advance.