I have had this happen! I ended up with three interviews the same weekend. I accepted the first one, and asked the other two about the possibility of alternate dates. Both additional schools are working with me on it. I didn't give one preference over the other due to my level of excitement, just the order the interviews came in. I told both schools right away that I had a scheduling conflict and left it at that.
I also received an invitation to a visit weekend yesterday after being admitted and it conflicts with two other schools that have back to back interviews. It happens. Just be up front with them!