One key question looming over the Republican tax proposal is how it will keep companies from fleeing the U.S., the same problem that has pressured Republicans and Democrats to seek action and that President Trump has frequently pledged to fix.

The uptick in corporate "inversions" and foreign takeovers, turning U.S. companies into Canadian, Irish and English businesses, has proved the top incentive for Congress to take on the monumental effort of overhauling the tax code.

Republicans say that lowering the corporate tax rate from 35 percent to 20 percent will help with that problem. But on another central consideration — how to tax international profits — the unified GOP framework announced last week is light on details, leaving lobbyists to guess how Republican taxwriters might try to solve one of the most tenacious problems in tax policy.

So far, the chairmen of the committees responsible for writing the legislation have declined to sketch out their plans.

"We're way ahead on it, but we still have to work through it. I know where we're going with it," said Sen. Orrin Hatch, a Utah Republican and chairman of the Senate Finance Committee, without offering further details.

The situation is an unusual feature of the U.S. tax system, namely the practice of taxing businesses on their foreign earnings at the corporate rate.

To avoid that tax, companies such as Apple, General Electric and Exxon Mobil have indefinitely deferred bringing earnings to the U.S., creating a situation in which corporations have an estimated $2.6 trillion in earnings overseas.

And more recently, businesses such as Pfizer have sought to move their headquarters to countries that don't have a worldwide tax to escape those taxes on international earnings.

Speaking at a hearing Tuesday on the international tax code, Sen. Rob Portman, R-Ohio, suggested that nearly 5,000 more companies would be headquartered in the U.S. if the country had had a 20 percent rate and a territorial system over the past 13 years.

"Our tax code could qualify for AARP benefits on the international side," he quipped.

As a solution, the GOP framework called for a territorial system in which companies are not taxed on the earnings of their foreign subsidiaries.

Yet it also suggested that foreign earnings would face a back-up tax to prevent gaming of the system, what it stated would be a reduced rate applied on "a global basis" — or a tax that kicks in if the companies have no tax liability overseas.

Lobbyists interpret that phrasing as a gesture at a global minimum tax to address the potential for the territorial system to actually exacerbate the problem, rather than solve it.

In such a territorial system, companies don't face additional taxes on foreign profits brought back into the U.S. Accordingly, the day that the GOP tax reform became law, tax lawyers at multinationals would begin strategizing about how to move accounts around to shift income to tax havens to cut overall taxes.

It's the kind of thorny issue that the border-adjusted tax originally championed by House Speaker Paul Ryan, and then killed by the retail lobby, was designed to address.

With a territorial system, Congress would have to design rules to prevent such abuse. Doing so would undercut the push for simplicity, but would be necessary to prevent companies from essentially stiffing the Treasury.

That's where the global minimum tax enters in. The idea is that it would penalize companies that reroute income to tax havens.

Yet there is little public information about how it would be levied and some suggestions that the GOP is not unified in its approach.

"I wouldn't characterize anything as a global minimum tax," Rep. Kevin Brady, the Texas chairman of the House Ways and Means Committee, said Monday. He added that his committee is writing international provisions to ensure that the country is not encouraging businesses to leave.

Addressing the problem of companies looking to move headquarters, jobs and patents overseas on CNBC Wednesday, Brady boasted that House Republicans aim to solve it in "a big, bold way."

At Tuesday's Senate Finance Committee hearing, a panel of tax experts warned Congress of one potential loophole in the joint framework on international taxes.

Stephen Shay, a Harvard Law School tax expert and former corporate tax lawyer, noted that if the global minimum tax is applied to corporations' total overseas profits, multinationals could game the system.

Here's how it works. A 13 percent minimum tax on a global business, for instance, would mean that a company that paid 25 percent of its earnings in taxes to foreign governments would not face any minimum tax. A company that did business mostly in the Cayman Islands, however, likely would pay only a pittance to foreign governments and would face most of the 13 percent tax when bringing profits back to the U.S.

Enterprising corporate lawyers would begin manipulating accounts and laws to make it appear as though their companies' income was earned in tax havens, right up to the point where their foreign taxes amounted to 13 percent of foreign earnings.

"People like myself in my prior career can blend high and low rates, and in some cases this will incentivize foreign investment," Shay told senators.

Instead, he testified, Congress should impose a minimum tax on a country-by-country basis. That way, for instance, corporations wouldn't benefit by routing income through Ireland, with its 12.5 percent corporate rate. That was the tack former President Barack Obama proposed, but was unable to enact.

Republicans haven't suggested they would follow that suggestion, and tax watchers expect that the plan might change as other features of the reform get hammered out.

"There's no easy way to figure it out until you start putting all moving pieces together," said Douglas Holtz-Eakin, president of the American Action Forum and an adviser to the Alliance for Competitive Taxation, a group of multinational corporations seeking changes to the international system.

It is likely that some possible reforms would gain the approval of some big businesses while upsetting others, based on whether they have large amounts of money unrepatriated, subsidiaries in tax havens and other considerations.

Inevitable disagreements are one reason that former Ways and Means Chairman Dave Camp included three options for treating international income when he drew up a tax reform plan in 2014.

Now, though, Republicans don't have time to fail to get it right on the first try.

Ryan said Tuesday that the Ways and Means Committee will introduce legislation within two to three weeks to have it signed by Trump by the end of the year. That means compressing months or years worth of negotiations and fine-tuning into the space of weeks, and then rushing it through Congress over the objections of lobbyists whose industries or companies would lose out.