Does Mumbai University allow the students to change the college after 1st semester?

Mumbai University allows such changes. One of my friends was studying in K.J. Somaiya college till the 4th semester of his BSc program and then switched to St. Xavier's College for semesters 5th and 6th.

It is important to note that Mumbai University does allow the candidate to change their college, however, the college that is your target may refuse to accept you. The college might have their reason to refuse the seat. So, at first, you need to ask if you will be allowed to get a seat in the college.

Before applying formally to the other college, you should get a NOC from your current college stating that they do not have any Objections to you seeking admission elsewhere. Using this certificate, you can apply for admissions to the college of your choice. You should not have any backlogs from your 1st Semester.

It would be really helpful if both the colleges are affiliated with the University of Mumbai. You should check if this facility is extended to different University systems as well before applying. There will be a lot of paperwork to do.