Republicans heading into conference on tax cut legislation are weighing a significant expansion of the part of the state and local tax deduction that would be kept in the bill, as one way of ensuring that residents in high-tax states get tax breaks, a key lawmaker said Tuesday.

“Possibly there’s four or five incentives — tax relief — that can help our high-tax states that we’re working with our lawmakers on,” House Ways and Means Chairman Kevin Brady told reporters at the Capitol.

Both the House and Senate bills mostly eliminate the state and local tax deduction, leaving only a deduction of up to $10,000 for property taxes paid to state and local governments.

Under current law, taxpayers can deduct both property taxes and income or sales taxes from their federal taxable income.

Brady, who will head the conference committee, said one option under consideration is maintaining the $10,000 cap, but allowing taxpayers to use it for income, sales and property taxes. That would be a “significant” expansion of the break, he acknowledged, requiring other parts of the tax cut to be scaled back. “It’s got a pretty big figure to it,” he said.

Other options that he mentioned are lowering individual income tax rates further or making the increased child tax credit available to higher earners.

The original bill authored by Brady would have eliminated state and local deductions altogether. The $10,000 property tax deduction was added back in to appease GOP lawmakers from states such as New York, New Jersey, and California, which feature high taxes. Maintaining or increasing that break could be necessary to keep those Republicans on board for the final bill.

The Senate amended its own version of the tax cut bill at the last minute to include a similar $10,000 property tax break.

But the Senate bill also included an additional hit to taxpayers in high-tax states by keeping part of the alternative minimum tax. Brady said House Republicans are likely to take the stance that the AMT should be repealed entirely.