You could make make it similar to the Canadian party system, where provinces have entirely different parties to the national ones (aside from the NDP). It may be that America's unique system of party Identity would hinder such a set-up.
It's not just party identity. It's the federal judiciary. We have a political system where the President appoints life-tenure magistrates to administer the provinces. Local parties just aren't viable. A country with a left-wing federal government and a variety of center-right localist parties is essentially just going to be a left-wing country (or vice versa) because of the federal judiciary coming in and doing what they feel like doing.
In Canada of course, a provincial legislature doesn't have to defer to federal courts on a variety of issues. Which is why Quebec hasn't gone buckwild.
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