I possible way would be to have candidates "scored" by voters. And delegates are given by total points. So a republican who wouldn't vote for Trump could give say Cruz 5, Rubio 4, Kasich 3, Carson 2, Trump,1 and a Trump voter may have gone Trump 5, Cruz 4, Rubio 3, Kasich 2, Carson 1. And in that tally Cruz would have 9, rubio 7, Trump 6 Kasich 5, carson 3. This may get a candidate who appeals to a broader spectrum of the base.
This is the exact voting mechanism we use in Ireland, and once you get used to it, the first past the post system used in other jurisdictions seems profoundly lacking. It's known as PR-STV, or Proportional Representation - Single Transferable Vote. Implementing this at all levels in the United States, from primary to general, would not only make elections more democratic, it would effectively eliminate the advantage that a nominee from one of the two dominant parties has over third parties - as third party voters could safely vote for their candidate without risking their vote assisting the election of their least favourite candidate. For instance, if somebody marked Stein 1, Clinton 2, Trump 3, then if Stein didn't get elected their number 2 would count as a vote for Clinton, thus preventing split votes from inadvertently boosting another party altogether.