Interest Rate Lock and Negotiating with Mortgage Broker

Okay, so I locked in at 6.125% with 0 points to purchase my new Brownstone in about a month. I am pretty happy with this rate, but would love for it to be at 6.0% or lower without having to pay points. Anyone ever negotiate with a mortgage broker after the rate has been fixed? What worked? I really like the broker, so I don’t want to play games, or is that what’s expected? Thanks.

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