Rate decrease exceptions?

Generally how many exceptions can brokers & mortgage advisors (from banks) make regarding the mortgage rates they offer to borrowers? I've already managed to get through two exceptions with a big bank, and now that the rates have dropped, I am tempted to try them again, but I am not sure what they might do if they say no. The broker that I had talked to mentioned that their lender is willing to do another (seemingly final) exception for me, which is 0.4% lower (which should reduce our monthly payment by ~$90 and for a 5-yr term saving around $2000 in interest.

I just don't know if I should use the rate of the broker to see if the bank will give me another go, cause while I haven't signed anything (closing in a month), it feels like I've committed with the bank already. Would appreciate your 2c