PhD application interviews on same day for different programs I'm not sure if anyone has experienced this type of issue or has advice, but I've noticed that many of the doctoral programs I'm applying to conduct interviews at the exact same time. I'm applying to about 11 programs, and 10 of them have 2-3 day trips between Feb 1st and Feb 15th. 

Granted, I will not get in everywhere, but I think there's a likely chance at least 2 or 3 interviews will overlap between schools. 

Is this a common issue? How do I approach a program that I get into (and am interested in attending) without saying "yeah sorry I'm interviewing for a different school on that date?" I would imagine that this would tick off the program and possibly leave me hopeless for that program even though I made it far enough to get an interview. Are programs flexible at all to students who can't make their 1-time a priori determined interview trip?
It's common. Departments aren't naive enough to think that they are the only place you've applied to. If you email them in good time and explain that you have another interview, I'm sure they will happily arrange alternatives. This could be a visit at a different, mutually convenient time, or perhaps a Skype interview.  Just phrase your email a bit more professionally than "yeah sorry I'm interviewing elsewhere" (but I'm sure you know this).

I would sincerely hope that no university is petty enough to put a black mark next to your name simply due to a clash of schedules -- but if they did, you don't want to work in such an environment anyway.