Here’s the dilemma for the Republican Party: Tens of millions of its voters support a candidate, Donald J. Trump, who rejects the organization’s values, reviles its policies and wants to kick its leaders out of power.

How does a once-proud party begin to recover from that?

In the latest episode of The Run-Up, we look at how — and even whether — the GOP can remake itself after enduring 16 months with Mr. Trump as its nominee.