As you asking for the names of the MBA colleges of Mumbai that accept the MAT Score the names of the colleges are as follow:

Top MBA Colleges

National Institute of Industrial Engineering, Mumbai
Shailesh J Mehta School of Management, Indian Institute of Technology, Bombay
SP Jain Institute of Management and Research, Mumbai
Jamnalal Bajaj Institute of Management Studies, Mumbai
Narsee Monjee Institute of Management Studies, Mumbai
Prin. LN Welingkar Institute of Management Development and Research, Mumbai
Sydenham Institute of Management Studies, Research and Entrepreneurship Education, Mumbai
IBS Business School, Mumbai
Tata Institute of Social Sciences, Mumbai
VES Institute of Management Studies and Research, Mumbai
Vidyalankar Institute of Technology, Mumbai
GNVS Institute of Management, Mumbai
IES Management College and Research Centre, Mumbai

some other good colleges of MBA in Mumbai are as follow:
BSE Institute Limited, Mumbai
Don Bosco Institute of Technology - MMS, Mumbai
Humera Khan Institute of Management Studies and Research, Mumbai
Indian Education Society's Management College, Dadar
Jankidevi Bajaj Institute of Management Studies, Mumbai
Kohinoor Business School, Mumbai
MISB Bocconi, Mumbai
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NL Dalmia Institute of Management Studies and Research, Mumbai
R.A. Podar College of Commerce and Economics, Mumbai
Regenesys Business School, Mumbai
S M Shetty College of Science Commerce and Management Studies, Mumbai
S P Jain School of Global Management, Mumbai