Donald Trump is a political independent who got elected as a Republican. He has embraced plenty of Republican positions, but he has never asserted himself as party leader. To state the obvious, Trump’s presidency is creating fissures, not unity, within the Republican Party. It’s even fair to ask whether he wants to lead the Republican Party — or any party at all.

President Trump is now mostly surrounded by able, committed advisers who — apart from Vice President Pence — have never been party loyalists. The reason: Being part of a political party, much less its head, does not suit Trump.

The White House flirts openly with the Freedom Caucus, whose sole function in Congress appears to be disrupting the druthers of House Speaker Paul D. Ryan (R-Wis.). Trump takes every opportunity to harass Senate Majority Leader Mitch McConnell (R-Ky.) and insult incumbent Sen. Jeff Flake (R-Ariz.). He made a deal last week on raising the debt ceiling and providing funds for Hurricane Harvey relief that stiff-armed his own party’s leaders and pleased “Chuck and Nancy” — the Democratic leaders Sen. Charles E. Schumer of New York and Rep. Nancy Pelosi of California.

Trump does believe in some Republican principles. He favors low taxes, a strong national defense, pro-business regulation and limits on immigration. What’s more, none of his independence has hurt GOP coffers. The Republican National Committee is far ahead of the Democratic National Committee this year — $86.5 million to $42 million.

But his flightiness has created odd diversions from the GOP mainstream and openings for marginal political characters. In my home state of Alabama, the bible literalist Judge Roy Moore — who’s claim to fame is refusing to remove a monument of the Ten Commandments from his court room — may become Alabama’s next senator (Disclosure: I have contributed to Moore’s opponent, Sen. Luther Strange). And in Michigan, because it seems either no one else is seeking the office or they are just intimidated, pop singer Kid Rock could be the GOP’s nominee for U.S. Senate.

All of which begs the question: How can the Republican Party and its ambivalent leader in the White House coexist?

The first answer is that Trump could never become a Democrat. There’s no such thing as a Trump Democrat.

So, what does it mean to have a mostly independent president? And what will the consequences be in 2020, the next presidential election year?

To be clear, Trump will run for reelection barring an earth-shaking change. And he will run as a Republican. But the Republican Party and the Republicans who run with him then won’t be the same as the party and the politicians who are around now. What we are witnessing today could be the most significant challenge to the two-party system since Teddy Roosevelt was nominated as the Bull Moose candidate in 1912.

The question Republicans need to ask themselves is this: Will Trump act more in ways that diminish their party or expand it? Finding a way to persuade the volatile president to become a benefit to the GOP rather than its gadfly should be job No. 1 for a sizable portion of the Republican leadership.