President Donald Trump and congressional lawmakers are not the only ones interested in collecting taxes on global profits that U.S. corporations are hoarding overseas. European regulators, knee deep in a campaign to stamp out tax avoidance, have their own plans for that money.

Last week, for instance, the European Commission billed Amazon for $293 million in unpaid taxes in Luxembourg, arguing that the country’s failure to collect the tax amounted to an illegal state subsidy. It also took Ireland to court for not following up on the $15.2 billion tax bill imposed on Apple last year.

“The Europeans are targeting U.S. dollars overseas that the U.S. believes should be taxed here,” said Dave Camp, a former Republican representative from Michigan who was chairman of the House Ways and Means Committee and author of an unsuccessful tax overhaul in 2014. “We have to address this problem before the Europeans get there first.”

The rulings on Amazon and Apple — which those companies are disputing — are byproducts of a race among governments to lure corporate giants to their shores in the hunt for new sources of revenue. That cutthroat competition is the reason that 73 percent of Fortune 500 companies have a subsidiary in a low-tax haven, according to the Institute on Taxation and Economic Policy.

That rivalry has the potential to fuel tensions between the United States and its allies. Yet it could turn out that the European crackdown on U.S. multinationals will ultimately help — rather than hobble — Washington’s efforts to get them to pay up. The harder that other countries make it for U.S. companies to take advantage of tax havens and sweetheart deals abroad, the weaker the incentives are for businesses to stash money out of the reach of the IRS.

Republican leaders have already put at the center of their tax rewrite an idea borrowed from Europe and other countries: Replace the system of taxing the worldwide profits of a domestic corporation with one that taxes only profits earned within its own territory.

“If we don’t move to a more modern system, we may lose the ability to gain that revenue,” Camp warned.

Multinationals will inevitably shop around for low rates. Americans and foreign companies have all played the same games, shifting patents and copyrights, profits and royalties to places with no or low corporate tax rates, like the Cayman Islands and Bermuda. (The IRS itself went after Amazon over assets it transferred to a Luxembourg unit, but Amazon ultimately prevailed.)

Efforts to cooperate have not always been successful, but there are signs that coordination can help. The Europeans’ effort is gradually shutting down the most notorious tax dodges that route corporate cash through Ireland and Luxembourg, said Michael J. Graetz, a professor and tax specialist at Columbia Law School.

“Those are like dinosaurs,” he said. “They’re moving towards extinction.”

And a new rule adopted by the Organization for Economic Cooperation and Development, requiring multinationals to report their income and tax bill in each country, will make it easier for the more than 60 governments that have signed on to monitor how much is actually collected.

So far, the team of Trump administration officials and lawmakers who drew up the latest framework for rewriting the tax code has released mostly general principles.

Now the IRS taxes the worldwide profits of American corporations, but the tax kicks in only after that income is repatriated to the United States. As a result, U.S. multinationals simply don’t bring much of it home. Republicans have made clear they intend to switch to taxing only profits earned within the United States, what’s known as a territorial system.

The $2.6 trillion in foreign profits that corporations already parked overseas in order to escape paying the IRS would be required to be repatriated — although taxed at a steep discount. And there are promises to prevent the tax base from shrinking, and discourage businesses from putting more operations and earnings overseas. At the same time, the official corporate rate would be slashed to 20 percent, from 35 percent, to make U.S. companies more competitive with their foreign rivals.

But this frame still lacks a picture, missing the details of how to accomplish those ambitious if sometimes conflicting goals.

Without tough safeguards, for example, the shift away from a worldwide system could end up curbing rather than promoting investment at home as American companies move even more operations overseas to avoid paying any U.S. taxes.

To some experts, like Kimberly Clausing, an economist at Reed College, the only way to prevent U.S. companies from exploiting loopholes in a new territorial regime is with a minimum tax. If a company’s tax rate fell below the floor in, say, Bermuda, it would have to pay the difference to the IRS.

Other experts, though, suggest borrowing another idea to broaden the tax base from foreign tax regulators — like more aggressive efforts to tax foreign multinationals.

As the Amazon and Apple cases show, “the politics in Europe are to tax somebody else’s multinationals, particularly ours,” said Graetz of Columbia.

“All of these other countries are basically trying to beef up and protect their tax base by ensuring foreign multinationals pay tax on income earned in their country,” he added, “and not on income earned by their own domestic multinationals.”

This is a different tack from the one taken in the United States, where tax dodges by homegrown billion-dollar corporations have been criticized for increasing the tax burden on companies that can’t shield assets.

The complaint that the U.S. tax code favors foreign multinationals over domestic ones did, however, arouse interest last week at Senate hearings on a tax overhaul.

“The United States corporate and international tax rules are an anticompetitive mess,” said Itai Grinberg, a law professor at Georgetown University. And one of their most senseless features, he added, is the tax advantage that permits foreign-owned corporations to artificially strip out their earnings in the United States.

Both he and Bret Wells, a law professor at the University of Houston, testified that foreign and American companies should be treated the same way.

Leveling the playing field does not necessarily have to wait for a rewritten tax code. Adam Looney, a former deputy assistant secretary for tax analysis at the Treasury Department, said the Trump administration could take a step now. He urged the president to reverse a decision to delay an Obama-era regulation to limit foreign companies’ tax advantages and prevent them from transferring out their earnings.

“Without the regulations, American-owned businesses will be worse off,” while foreign multinationals avoid about $7.4 billion in U.S. taxes, Looney wrote this week in a policy brief for the nonpartisan Brookings Institution.

The delay, he said, means that the United States is, in effect, paying “foreign investors to take over our companies with our own tax dollars.”

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