Hello

With 95+ percentile in CAT exam, you can expect a call from IIM Kozhikode, IIM Shillong, IIM Ranchi, IIM Rohtak, IIM Udaipur, etc.
You can go through the link below and check the list of colleges which you can expect according to your CAT percentile-

 https://bschool.careers360.com/articles/which-b-schools-can-i-get-if-my-cat-percentile-between-90-and-100

Good luck!

Each IIM has its own admission criteria, Most of the IIMs give maximum weightage to Personal Interview and CAT score for admissions. However, factors like academic cut-offs, past academic performance, relevant work experience, gender diversity etc. also play a major role in the final selection. Based on all this factors the students are called for interview and WSAT round. 

If you are expecting 96.7 percentile in CAT, you should have the decent chances to get a call from New IIMs. You can also prefer the below given article for the further information.

https://bschool.careers360.com/articles/iim-admission-criteria

Good Luck!