A selection organization and system rather than a political party?
precinct, county, region, state, national region, national
And then the issue becomes how to keep it from becoming a party.
Actually that is what the Electoral College was all about. Local people would elect people they thought were like minded and all those like minded people would go to the electoral college and find someone who would make a good president. Then they decided to have direct elections of candidates who would choose their own electors. It went from a bottom up electoral process to a top down.
And then the issue becomes how to keep it from becoming a party.
I don't think it is possible unless we revert back to the original electoral scheme.