For 4th year electives I used VSAS (
https://services.aamc.org/20/vsas/) to do anesthesia/critical care rotations at local university hospitals. You basically just fill out an application, submit your resume, and the rotation site either accepts or rejects you. I was accepted everywhere I applied. Most places do not take 3rd osteopathic students, so I didn't use that program for my 3rd year electives. Instead, I used a list of provided electives affiliated with my school and I just called the phone number provided. I have no experience finding 3rd year core rotations.