Hey,
Few colleges not surely IIM- can take you if your percentile is somewhere near 80–85

Institute for Financial Management and Research

K. J. Somaiya Institute of Management Studies and Research, Mumbai

FMS, BHU

XIME

Great Lakes, Chennai

You can check your best possibilities with CAT Pathfinder tool.

https://bschool.careers360.com/pathfinder/cat

Hope this helps.