Psychology

Yes, you can definitely pursue M.A. in psychology. Already having done MBA which gives scope for many opportunities, you need to have a better clarity as why you want to pursue a career in Psychology. Psychology is one of the interesting field to study and practice as a career.

Yes, Jain University offers M.Sc. Psychology is Integrated with British Association of Counselling & Psychotherapy, UK. The eligibility criteria is given below.
Eligibility : The minimum qualification required to apply is a bachelors degree in the respective discipline from a recognised university.

https://www.shiksha.com/humanities-social-sciences/psychology/colleges/b-a-colleges-india
Here is the college list for distance education available in B.A. Psychology.

The CRC or the placement cell of Amity Mumbai are always in search of good internships and placements for their students. The internship offered by Amity Mumbai is at great hospitals, rehab centres, under renowned psychologist/psychiatrists. I am not really sure of placement possibilities in Amity Mumbai for Psychology as there are very few places which take students after graduation. Even if they're there, they might pay you very less.

Very few colleges are available in India wherein Psychology, the core subjects are taught. Amity is one amongst them where you have core subjects in Psychology. The crowd is really nice and so are the teachers. The teachers have impeccable knowledge and they also, sometimes, give free counselling sessions to the students in need. The infrastructure in Amity is just Hi-tech with AC filled campus. I really think it is a great idea to pursue psychology from Amity Mumbai.