Although Trump has yet to announce his entire team, his selection of his cabinet so far has been assailed by Democrats and his critics. His naysayers say people who have been handpicked by Trump to hold key judicial and diplomatic posts under his administration have dubious antecedents.
Trump has also moved to mend fences with moderate Republicans as he goes about building a new administration, interviewing one-time foe Mitt Romney for secretary of state, and inviting his ousted transition chief Chris Christie for a sit-down Sunday at his Trump National Golf Club.
Vice president-elect Mike Pence informed that Trump's critic Mitt Romney was also under "active consideration" to become the next Secretary of State.
He and Vice President-elect Mike Pence began their day attending a Sunday service at a Presbyterian church in the New Jersey countryside.
The 70-year-old Republican billionaire promised reporters they would "hear some things" after a second marathon day of meetings at his New Jersey golf retreat, a 90-minute drive from Manhattan.
"General James 'Mad Dog' Mattis, who is being considered for Secretary of Defense, was very impressive yesterday. A true General's General!" Trump said on Twitter.
The 66-year-old Mattis, who called Trump "the real deal" after their meeting Saturday, is a retired Marine Corps general who led the US Central Command from 2010-2013, overseeing the US withdrawal from Iraq and a surge in Afghanistan.
A colourful combat commander and voracious reader, he has been quoted as saying, "Be polite, be professional, but have a plan to kill everyone you meet."
Chris Christie, who threw his support to Trump after his own bid for the Republican presidential nomination fizzled, appeared back in favour after being pushed out as transition chief.
The New Jersey governor has been under a cloud over a scandal involving the closing of a major bridge linking New York and New Jersey, allegedly to punish a Democratic mayor. Two former Christie aides were recently convicted in the case.
Asked on Saturday if "Bridgegate" disqualified the governor from serving in the cabinet, Trump retorted: "We like Chris a lot."
Others meeting Trump on Sunday include former New York mayor Rudy Giuliani; immigration hardliner Kris Kobach; Wilbur Ross, under consideration for commerce secretary; global investor David McCormick and conservative writer John Gray.
Trump will also meet with Bob Johnson, the founder of Black Entertainment Television (BET) who has urged African Americans to vote for their best interests rather than be wedded to any political party.
Exit polls showed some 88 percent of African American voters supported Democratic nominee Hillary Clinton versus just eight percent for Trump.
Trump's interview with Romney, the 2012 Republican presidential candidate who called him a "fraud" during the campaign, suggested to some observers that he is looking for a mix of views despite the hard-line cast of his national security team so far.
Romney himself said nothing after Saturday's session. But Pence confirmed that Romney was under consideration for secretary of state, a post also sought by Giuliani and others.
Trump's picks so far include ultra-conservative Senator Jeff Sessions as attorney general, hawkish congressman Mike Pompeo as CIA director and retired lieutenant general Michael Flynn as his national security adviser. His choice of Steve Bannon, seen as an ideologue of the ultra-conservative alt-right movement, as chief strategist has also drawn fire.