can i transfer from one private university to mumbai university after completion of 1st year ? can i get admission in 2nd year?
Nope! You can't do that. This kind of things occur when you read under a college of the same university and if you want to change your college then you can avail admission to the 2nd year of another college only if that college is also affiliated by the same university. But this kind of rules don't occur for separate university/colleges. But if you wish you can always take admission in the first year of the course but lateral entry to 2nd year won't be possible.
To know more about MU visit the link below:
https://www.careers360.com/university/university-of-mumbai-mumbai
I hope this answer helps. All the very best for your future endeavors!