If taxing foreign earnings that have already accumulated overseas is difficult, so is eliminating incentives that reward companies for continuing to keep profits in tax havens. To that end, Mr. Trump and the Republican leadership have pushed to slash the corporate tax rate and switch to what is known as a territorial system that would tax only profits earned in the United States and not those earned in other countries.

Mihir Desai, an economist at Harvard Business School, likes that approach. “We currently have the worst of all worlds,” he wrote in an email. “We have a high marginal rate,” which encourages companies to avoid taxes and puts the United States at a global disadvantage.

“And we have low average rates” — because of all the loopholes — “which indicate that we’re not collecting as much as we used to, given the very high level of corporate profits.”

The crucial questions are how to pay for a lower rate and how to prevent abuses. Corporate tax cuts that lead to huge deficits could hobble the economy. And a territorial system without sufficient safeguards could end up encouraging even more businesses to shift profits, operations and jobs to countries with lower tax rates.

Other nations with territorial systems have tried to prevent companies from wriggling out of paying taxes, while tax experts have suggested proposals ranging from a minimum global tax to tighter rules to prevent companies from relocating their patents and copyrights to tax havens like Bermuda and the Cayman Islands.

But skeptics worry that making the system airtight is impossible. “It’s an endless cat-and-mouse game,” said Matthew Gardner, senior fellow at the Institute on Taxation and Economic Policy, a research group based in Washington. “What’s driving companies to engage in paper transactions is not our 35 percent tax rate,” he said, but other countries’ willingness to undercut whatever rate the United States settles on. “You can never win if you are competing against their zero tax rate.”

Mr. Gardner argued that a broader definition of American competitiveness is needed that includes not only the tax system, but also the business infrastructure that the tax system supports — bridges and roads, health care, education and research and development. “If all you think about is the tax rate, then it should be zero,” he said. “Competitiveness is about finding the right balance.”