The Labor government requires two more upper house votes to pass the legislation finalising the merger of the University of Adelaide and University of South Australia, meaning it needs only court either the Liberals, the Greens or SA Best.
Ahead of the release of a report by a joint parliamentary committee into the move on Tuesday, Greens and Liberal members of the inquiry both said their votes were up for grabs, as long as proposed demands to amend the bill are met.
SA Greens education spokesman Robert Simms called on the universities to make the business case for the merger public.
"It's public money and the community has a right to know," he told ABC Radio.
A recent report by the Australia Institute found 86 per cent of South Australians wanted to see the business case amid growing concerns about the secrecy of decision-making behind the nation's largest tertiary educators.
Mr Simms also has reservations about what the merger means for the student experience, job security and changes to university governance.
"We've still got issues that we're going to raise and I'll be looking at some potential amendments," he said.
Shadow education minister John Gardiner said his party saw significant upside in the move for the SA economy but flagged additional concerns he wants addressed.
The risk of integrating two major institutions with differing cultures and the potential to distort the broader higher education sector caused him particular unease.
"If this goes badly and the university's desired increased income doesn't work out, then it could be a disaster," he told ABC Radio.
The committee, which ran from August to October, heard the merger could provide more funding for productive research and give SA vital skills needed to deliver the AUKUS program.
But it also heard some staff had concerns it could precipitate a major exodus of top staff, damaging the reputation of the institution.
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