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you refi and take out more money to get that tax bill down
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I don't think so, goaliedad. The home's assessed value remains the same, regardless of how much or how little you owe on it. The only thing that makes tax bills go down (I'm talking about real estate taxes here) is if the value of the house goes down, which has of course happened to many people recently.
Paying more and more interest on a larger and larger loan seems a dubious way to increase deductions and therefore reduce income taxes. Someone's not looking at the net expense there.