I know a few people from MUHS Maharashtra and they were able to provide some information regarding the second-year transfer. According to them, students from private colleges affiliated with MUHS are eligible for second-year transfer. You can’t transfer from deemed universities. 

After the declaration of first-year results, MUHS puts up a notification for transfer on their website. They make a list of all applicants and they will call you in for an interview. In the interview, they usually ask why you want to change your college. 

In order to transfer, vacancies should be there in your desired college. Also, students with better marks are given preference. You will need No Objection Certificates (NOC) from both colleges. If you have contacts in the college you want to join, it can be helpful.