WASHINGTON — For the billionaires, the multimillionaires and the plain well-off people whom President-elect Donald J. Trump is choosing for his cabinet, the first step to office will be the sort of grilling he didn’t face — on potential business conflicts of interest and, for some, tax returns — courtesy of the Senate sleuths who have taken their toll in the past.

President Obama’s first Treasury secretary, Timothy F. Geithner, was nearly derailed in 2009. His first choice for secretary of health and human services, Tom Daschle, did not make it through that year.

Now the billionaires Betsy DeVos, Linda McMahon and Wilbur L. Ross Jr., and the multimillionaires Ben Carson, Elaine Chao, Steven Mnuchin, Representative Tom Price, Andrew F. Puzder and Todd Ricketts can expect much of the same scrutiny.

“With the president-elect flouting a 40-year bipartisan tradition of disclosure and transparency, we think it’s more important than ever to ensure that senior officials across government aren’t operating under a different tax code than everyone else,” warned Senator Ron Wyden of Oregon, the senior Democrat on the Senate Finance Committee, which has upended its share of nominees.

After nearly two centuries in which Senate reviews were cursory at best, that confirmation process has become increasingly arduous, regardless of party, and especially in the committees that require nominees’ tax returns.

Dean Zerbe, a former counsel to the Finance Committee, had some advice for Mr. Trump’s nominees facing that panel: Do not copy the president-elect’s defiance on disclosure. “The committee will say, ‘Bless your heart. Now send us your tax returns,’” Mr. Zerbe said.

Senate Democrats will be pressing in January to make the scrutiny even broader. They propose that all committees make nominees privately submit their three most recent federal tax returns. Three committees — Finance, Budget, and Homeland Security and Governmental Affairs — already do so. Together they have responsibility for examining five cabinet-level officials before confirmation: the secretaries of Treasury, health and human services, and homeland security, and the president’s trade representative and budget director.

For Democrats, the tax-disclosure proposal is a way to underscore Mr. Trump’s refusal to release his returns, despite a four-decade tradition of presidential candidates doing so. More to the point, they will have ample opportunity to press home their contention that a number of his cabinet choices have wealth and backgrounds at odds with his populist pitch.

“He is building an administration that looks a whole lot like himself,” said Senator Patty Murray of Washington, the senior Democrat on the committee that will handle the nominations of Ms. DeVos, who married into the Amway fortune, as education secretary, and Mr. Puzder, a fast-food executive, to be labor secretary.

Those nominations will go to a committee that has not previously required nominees to file tax returns along with other financial disclosures. So will those of Mr. Ross, an investment titan chosen for secretary of commerce; Mr. Trump’s choice for deputy commerce secretary, Mr. Ricketts, the heir to the Ameritrade fortune; the pick for transportation secretary, Ms. Chao, a wealthy former labor secretary and the wife of the majority leader, Senator Mitch McConnell of Kentucky; Mr. Carson, a retired neurosurgeon;…