Do I negotiate a raise before or after signing a contract with a new company?

I got a job offer elsewhere (yay!). I want to make a last ditch attempt to negotiate with my current company - my boss is attempting not to give me a promotion or raise, despite telling me how much easier I make her work life...

Anyway, do I try and negotiate a raise before or after I sign the other job contract? Sorry, I know this is a dumb question, but I've never done this so I'm not sure.

Thank you!

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