Australia's big four banks would be carved out of the government's corporate tax cut package under a proposal designed to woo crossbench support.
Finance Minister Mathias Cormann on Tuesday secured the Senate's support to debate the plan to exclude Commonwealth Bank, ANZ, NAB and Westpac.
He has made the offer to key crossbenchers, including One Nation leader Pauline Hanson and her colleague Peter Georgiou.
But the changes don't extend to capping the tax rate being cut from 30 to 25 per cent for businesses with $500 million - as suggested by independent senator Derryn Hinch.
"The government did propose to One Nation that we would be prepared to carve out the big four banks," Senator Cormann told parliament on Tuesday.

One Nation party leader Pauline Hanson wants to see the detail of the government's offer to exclude the big banks from tax cuts. Source: AAP
But Senator Hanson claims she couldn't support the compromise because One Nation wasn't shown draft laws.
"In a parting comment by Minister Cormann, he suggested carving out the banks to secure One Nation votes, to which I said my decision was firm," Senator Hanson said in a statement.
"No draft legislation was ever received and I can confirm Senator Georgiou did not receive this alleged document either."
The corporate tax cuts survived an initial Senate vote on Tuesday, allowing the government to try to amend the bill to exclude the big banks.
The move would save the budget $7.9 billion to 2027/28.
Senator Cormann called on Labor to support the changed tax plan.
"If you were genuinely concerned about a tax giveaway to the big banks, you'd now have the opportunity to vote in favour of this amendment," he said.
Parliament has already agreed to deliver tax relief to companies with an annual turnover of up to $50 million, but the 25 per cent rate will be brought in gradually.
Labor estimates bringing forward tax cuts for businesses turning over under $50 million could cost the budget $1.8 billion over the next four years, and $6.5 billion in the medium term.