With Labor firmly opposed to the package, government negotiations on Wednesday landed the 10 crucial votes of One Nation, the Nick Xenophon Team, Jacqui Lambie, Derryn Hinch and Lucy Gichuhi.
Greens leader Richard Di Natale was in talks with the government about extra money for students with disabilities when Finance Minister Mathias Cormann flagged in parliament a deal had been struck with the crossbench.
The debate will likely continue well into Thursday, the final scheduled sitting day before the winter break.
While the government has not publicly released its amendments, Senator Xenophon told reporters an agreement had been struck to shorten the funding rollout from 10 years to six and put in place an independent watchdog.
"This will unambiguously lead to a better outcome for our children," he said.
Senator Xenophon said this would mean $23 billion in extra funding to schools - instead of $18.6 billion - delivered faster than originally planned by the government.
The government had also agreed to the new watchdog conducting a review of the schooling resource standard, which is the basis of the new needs-based funding model, and a guarantee the states won't withdraw their funding as more federal money flows through.
Catholic and independent educators appeared to have had a win, with the government reportedly agreeing to a $50 million transition package over the next 12 months.
However, the National Catholic Education Commission said in a statement it had not had any formal or informal contact from the government on the latest proposal.
"The minister continues to run a 'policy via the media' approach and is using that strategy to confuse his colleagues in the Senate and give the impression he has in some way addressed the concerns of the Catholic education sector," NCEC director Christian Zahra said.
Senator Di Natale told reporters if the final legislation included a special "carve out" for the Catholic sector his party could not support the amended bill.
"We can't support legislation that is not genuinely needs-based and sector- blind."
Senator Lambie told reporters her vote on the bill was a "yes at this stage".
Asked what extra money had been put on the table for her state of Tasmania, Senator Lambie said: "There is no figure or money. I'm still in discussions."
One Nation leader Pauline Hanson said while she backed the bill, the government should consider as part of its reforms putting disabled and autistic children in special classrooms.
"It's no good saying 'We've got to allow these kids to feel good about themselves and we don't want to upset them and make them feel hurt', and I understand that," she said.
"But we have to ... consider the impact that is having on other children in that classroom."
Labor leader Bill Shorten said such comments were "heartbreaking and upsetting" for parents.
Mr Shorten said the government should scrap its legislation and start again, arguing it short-changed schools by $22 billion.
