I think that depends on how you prioritize the programs according to your own interests. You can ask to extend the timeframe, but a few people already ran into weekends getting full. For my UNC interview, they gave me two choices, but they were in conflict with two other interview weekends of mine. I asked if they had any others, they gave me a third option and that's the one I switched to. There's no harm in asking if there's other options, especially if you're really interested in the Emory and Duke programs.