I know someone who is finishing a postdoc in mathematics and is in the thick of the tenure-track job search. He had something like 15 interviews at the Joint Mathematics Meetings (JMM) last week. At the moment he has four invitations for on-campus interviews. Of these, exactly one is one of his very top choices. He sent me a list of seven institutions at which he had JMM interviews, has not yet received campus interviews, but would prefer them to some of the places for which he has received but not yet accepted interviews. He is getting worried that he could book too many interviews at these less desirable places and then be boxed out of later interviews to come. By the way, I think he is excellent and unusually broadly appealing, and I absolutely expect him to get more on-campus interviews than he now has. I don't think I have heard of people who have actually booked so many interviews that they have no slots left, and I am tempted to tell him not to worry so much about that -- the calendar is full of days -- but I suppose it could happen in his case. What do you think he should do, e.g. how should he respond to two on-campus invitations that are less desirable than many of the JMMs he's waiting on?
Here is what I said so far:
1) Contact all seven desirable places, let them know the situation, and see if he can shake loose interviews from them or at least information about timing of the interviews.
2) Countenance the possibility of cancelling a job interview if he really does get booked solid.
I am not really sure about 2). Clearly you should cancel all interviews once you've accepted a job, and cancelling interviews when you already have an offer in hand makes just as much sense. I'm not sure about the ethics of cancelling an interview to take another interview instead. Is this commonly done? Would it annoy people or look shady to some? If this is going to be viewed as dishonorable behavior even by some, I think he would really like to know that: he is as "fully honorable" as anyone I've known.