They could just choose blanket primaries, like California has: https://en.wikipedia.org/wiki/Nonpartisan_blanket_primary After the blanket primary, the final election is between the top-two, regardless of their party affiliation.
The effect in California seems to have been to make the state even bluer, but arguably that's because rather than being forced to choose between Republican and Democratic standard bearers, the system returns some advantage to more moderate candidates, just within the field of Democrats (increasingly many of whom were once registered as Republicans). Unless you want to run on stereotypical Republican issues (abortion, religion, etc), your best bet strategically where the electorate is already majority Democratic is to run as a Democrat, regardless of your policies, which is not an option where candidates have to worry about being "primaried".
Ranked-choice is even better, of course, but I think you can see a similar dynamic wrt the candidate pool shifting Democratic.
I'd argue Alaska's system is even better. They have a top-4 jungle primary. Everyone focuses on the ranked-choice voting general election they have that follows, but I think letting 4 candidates advance out of the primary is an improvement because it weakens the primary electorate's power to eliminate candidates early. And as mentioned, the primary electorate is tiny and probably not representative of the population as a whole.
The effect in California seems to have been to make the state even bluer, but arguably that's because rather than being forced to choose between Republican and Democratic standard bearers, the system returns some advantage to more moderate candidates, just within the field of Democrats (increasingly many of whom were once registered as Republicans). Unless you want to run on stereotypical Republican issues (abortion, religion, etc), your best bet strategically where the electorate is already majority Democratic is to run as a Democrat, regardless of your policies, which is not an option where candidates have to worry about being "primaried".
Ranked-choice is even better, of course, but I think you can see a similar dynamic wrt the candidate pool shifting Democratic.