Does Deloitte USI Renegotiate?

I am having offer of Deloitte USI with 9.7LPA total. At the same time I am also having offer from mid size company of 10.65 LPA. I really want to Join Deloitte USI. I got selected for Analyst level . Will Deloitte revise the offer? I told the same thing to HR, She told to share counter offer. I shared on Tuesday then she told she will get back to me by Wednesday. It’s friday now. So till when can I expect a response. She told she will check with Business. If it has happened with you the after how many days your offer got Revised?