House Republicans should slow down their consideration of a tax-overhaul bill after investigative reports Sunday alleged offshore tax-avoidance by U.S. multinational companies including Apple Inc. and Nike Inc., congressional Democrats and tax-advocacy groups said.

But the Republican chairman of the House Ways and Means Committee indicated Sunday that the panel would stick to its plans to consider the bill this week. Representative Kevin Brady said he believes lawmakers “have a pretty good handle” on how to address the erosion to the U.S. tax base that results when corporations shift profit offshore. House leaders want to pass the bill by Thanksgiving, in roughly 2 1/2 weeks.

The bill that Brady released last week would impose a 20% excise tax on certain payments that U.S. companies make to overseas affiliates—a potential source of profit-shifting to tax havens. It also called for a tax of roughly 10% on some foreign profits for corporations going forward. The excise tax measure has already drawn opposition.