Let’s not conflate with your original question. “What other schools” is more about yield management and marketing than collusion.
Feel free to not answer it. But the whole “what other schools” discussion has been covered many times. Here’s the most recent example:
http://talk.collegeconfidential.com/prep-school-admissions/2120104-application-question-what-other-schools-are-you-applying-to.html
Google is your friend. Here’s a start:
https://www.nytimes.com/2018/04/10/us/politics/justice-department-probe-college-early-decision.html