I had to reschedule one of my interviews for the same reason.
I told them that I had a previously scheduled interview on the date (I had scheduled it about 2 weeks prior). I was told that the Admissions Committee would have to choose a new date for me - I didn't have any options. It took them about a month to get back to me with a new date, and they wanted me to come in 2 weeks (kinda short notice, but it worked out).
On the other hand, when I called a different school to change the date, I was able to give them 3 dates that worked for me, and they called me the next week with an interview on one of the days that I picked.
I think most schools are pretty nice/flexible about changing dates. The first school that I talked about seemed to be the only exception that I've run into.
Good luck and congrats on your interviews!