Harvard University is looking for a new leader. So is the University of Pennsylvania. And Yale University. And Stanford University.

While plenty of college presidents retire or resign every year, it’s rare for so many prestigious research universities to be simultaneously hunting for replacements. And leading these schools is not the same job it was a generation ago. Bill Funk, founder of higher-education executive search firm R. William Funk & Associates, likened the position to being a professional fundraiser and public relations executive combined with the mayor of a city.