WASHINGTON — His nascent administration already under attack, President-elect Donald Trump was considering Monday whether to inject new diversity into the GOP by recommending a woman to lead the Republican Party and an openly gay man to represent the United States at the United Nations.

The moves, among dozens under consideration from his transition team, follow an intense and extended backlash from Trump’s decision Sunday to appoint Steve Bannon.

Trump was considering tapping Richard Grenell as U.S. ambassador to the United Nations. He would be the first openly gay person to fill a Cabinet-level foreign policy post.

Grenell, known in part for aggressive criticism of rivals on Twitter, previously served as U.S. spokesman at the U.N. under President George W. Bush.

Trump was also weighing whether to select Michigan GOP chairwoman Ronna Romney McDaniel, a niece of chief Trump critic and 2012 presidential nominee Mitt Romney. She would be the second woman ever to lead the Republican National Committee – and the first in four decades.

“I’ll be interested in whatever Mr. Trump wants,” McDaniel said Monday, adding that she was planning to seek the Michigan GOP chairmanship again.

Appointing McDaniel to run the GOP’s political arm could be an effort to help the party heal the anger after a campaign in which Trump demeaned women.

The appointment of Grenell, who has openly supported same-sex marriage, could begin to ease concerns by the gay community about Vice President-elect Mike Pence’s opposition to same-sex marriage during his time as Indiana governor.

The personnel moves under consideration were confirmed by people with direct knowledge of Trump’s thinking who were not authorized to publicly disclose private discussions. They stressed that the decisions were not final.