I wouldn't play it that way. You agreed to a salary with the new company. Going back for more after you have a deal in place would be a crappy way to start. The better play is to give the old company the number they asked for. What would it take for you to pass on this new opportunity...no matter how high it is. If they say yes then you just earned a fat raise. If they say no there's another, more attractive company that wants you.
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