Independent senator David Pocock is joining a push to resolve a stalemate over the Albanese government's signature $10 billion housing fund.
The government tried to bring on a vote in the Senate on Wednesday for the Housing Australia Future Fund, which would build 30,000 social and affordable homes.
But the Greens and the coalition prevented a vote from taking place.
Senator Pocock is pushing for amendments to the bill to include an ability to periodically increase the $500m annual cap on disbursements from the fund, and indexation at 2.5 per cent each year.
Senator Pocock said it made "no sense" for the government to have to change legislation every time the investment fund had a good year.
"From day one I have backed calls from right across the residential and community housing sector for more ambition when it comes to the Housing Australia Future Fund," he said.
"But I have also been clear that I'm hearing from my community that they want to see legislation pass that will start building houses."
He said indexation of the cap was also crucial to attracting the investment needed in new social and affordable rental homes.
Greens housing spokesman Max Chandler-Mather said the crossbench had managed to negotiate amendments to several pieces of legislation, and accused the government of not taking meaningful action to address the issue.
"This is the worst housing crisis Australia has faced in a long time and it's actually quite important that we start to take this seriously," he told Sky News.
"We feel compelled to make them (Labor) ... negotiate properly to guarantee a package that actually starts to put roofs over people's heads."
Labor minister Tanya Plibersek said the party was being "typical Greens" and stood in the way of progress being made on issues they were invested in.
"Now in housing, they say they want more investment in housing but they're voting against tens of thousands of affordable homes," she told Sky News.
"It's extraordinary that you've got a Greens housing spokesperson that says he wants more homes but ... is actually opposing the building of new homes in his in his own backyard."