While I agree with much of this poster's original message - I really discourage the above referenced suggestion. Please don't make something up!
I'm a 5th year in a clinical phd program, and have been on the other side of 4 interview weekends. Everyone knows that schools are interviewing around the same time, and will likely see through any made up story. You will either appear unreliable (read, a liar), or possibly daft for scheduling some other 'travel' when you'd presumably be going to interviews!
The important thing to know is the inability to attend a specified interview date due to other interviews is quite common. Some programs (like mine) will let you come in person on another day. We only accept 4-6 students a year, and I have known more than a few of my classmates who interviewed on a separate day than the large group. Having that said, I would pick your favorite (as the other poster suggested) and go to their scheduled interview day - as you often don't get to meet everyone (particularly the other students) when you interview separate from the group. The fact that you have other interviews does not make you appear less desirable, in fact I would argue the opposite.