The change appears to be designed to earn support from Sens. Ron Johnson , R-Wis., and Steve Daines , R-Mont. Both senators argued that pass-through businesses would not get as much relief as corporations under the Senate plan.

A tweaked Senate tax bill would increase the income tax deduction for pass-through businesses to 20 percent from 17.4 percent, Bloomberg and Politico reported, citing unnamed senators. It would not change the headline rate at which those entities' income is taxed.

Senate Republicans will move to ease the tax burden on pass-through businesses under their bill, one of a series of expected changes in a push to win over skeptical lawmakers, two news outlets reported Wednesday.

Shortly after the reports, Daines tweeted that he will vote Wednesday in favor of starting debate on the bill. He said he saw "some good progress for Main Street businesses in the tax cut bill."

Pass-through businesses are not corporations and get taxed at individual rates. While those entities include small businesses, most pass-through income goes to the top 1 percent of American earners, according to research cited by The New York Times.

The Senate plan would tax pass-through businesses at individual rates but allow the deduction. It includes some restrictions to deter wealthy people from abusing those benefits.

A similar bill passed by the House would change the pass-through income tax rate to 25 percent.

Both Johnson and Daines previously said they opposed the Senate plan as written. On Tuesday, Johnson voted to advance the bill from the Senate Budget Committee, saying he got assurances that his concerns would be addressed.

Senate Republicans aim to pass their tax proposal this week and cannot lose more than two votes.