>It depends on the state. In some states you can as in North Carolina. In others you can only vote in the primary for your party candidates. You cannot switch parties or vote outside of it. In others, you can register for any party at the caucus/primary and vote in that party even if the day before you were registered to another party.
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Pretty much everywhere, you can switch parties. The question is when. Here in PA, we have a closed primary and registration for the election ends several weeks before, presumably to allow time to print out the binders we sign when we vote and get them to the polling places.

Tamar