One is that the United States and Eritrea are the only countries that tax the worldwide earnings of their citizens even if they live abroad.

Alex Marino, who heads one of the largest expatriation legal practices in the world for Moodys Gartner Tax Law, said that in the final quarter of 2016, when Donald J. Trump was elected president, there was a record spike in the number of Americans renouncing their United States citizenship. But the biggest driving force by far, he said, “is finances and taxes, rather than politics.”

Peter Vincent, a former senior prosecutor in the Obama administration who now oversees security liaison for Henley & Partners, the law firm, said another factor was personal security.

“There are some places in the world where if your taxi or bus gets pulled up and you are carrying a U.S. passport, that is a death warrant,” he said, “so people prefer to have a second passport for safety reasons.”

Knight Frank, a British real estate consulting firm that operates globally, estimated late last year that 36 percent of people with more than $30 million in net assets had second passports, up from 34 percent a year earlier.

Christian H. Kälin, the Swiss-born lawyer who leads the British-based Henley & Partners, said the trend was also growing among the less wealthy.

For those seeking residency visas or passports, the firm charges fees that start at about 20,000 euros, or $22,500, and can reach €500,000 for complicated programs like that of Austria, which requires nonproperty investments of at least €10 million. The firm has grown rapidly over the past decade, expanding to 30 offices around the world.