A North Dakota initiative petition has been submitted. It would establish a top-four system. The general election would include ranked choice voting, but the primary would not. See this story.
There would be no party nominees if this initiative passed and took effect (except for President), but the initiative backers did not come up with any new method to define “political party”. Current law says a party remains on the ballot if it polls 5% for Governor, President, Secretary of State, or Attorney General. But under this initiative, there would be no party showing for any of those offices except President.
North Dakota doesn’t have party registration, and already has an open primary. Any voter is free to choose any party’s primary ballot.