Prime Minister Anthony Albanese is being urged to make two key changes to how ministers are appointed in the wake of the fallout from Scott Morrison's secret appointments.
Mr Morrison took on the health, finance, treasury, home affairs, industry, science, energy and resources portfolios between March 2020 and May 2021.
Mr Albanese will receive advice from the solicitor-general on Monday on whether the former prime minister's actions gave rise to any legal or constitutional problems, then make any necessary changes.
University of Sydney constitutional law professor Anne Twomey said two steps could be taken to make the system more transparent.
She said the commissions handed to ministers by the governor-general to administer departments needed to be published in the Federal Register of Legislation.
And the arrangements made between ministers within portfolios which divided responsibility should also be made public.
"There are holes in the system and the best way to try plug them is to be increasing transparency in relation to who holds the power to administer various departments and exercise statutory power," she told AAP.
The prime minister chastised his predecessor for making light of his actions.
Mr Morrison commented on memes and posted photoshopped images of himself in various groups, including as the coach of the NRL's Cronulla Sharks.
"This undermining of the parliamentary system of government, of the whole Westminster system and our democratic traditions of accountability, are something that aren't a laughing matter," Mr Albanese told the ABC.
"I'm somewhat surprised that there's been no concept that there's a need to say to the Australian people that the wrong thing was done."
Liberal deputy leader Sussan Ley said it was "the great Australian tradition to take the mickey out of yourself".
Liberal senator Simon Birmingham said Mr Morrison got the "big calls" right, which included the COVID-19 pandemic, and deserved that to be "the main part of his legacy".
However, he told Sky News: "On these administrative arrangements around the administering of different departments, he clearly got some things wrong."
Former coalition government minister Angus Taylor said he didn't think it was necessary for Mr Morrison to apologise to him for secretly taking on his portfolio.
"My working relationship with him was very positive," he told 2GB.
Australian Republic Movement deputy chair Meredith Doig said the revelations were a demonstration of a "broken" system.
"What we've learnt is that we can't rely on the old constitutional conventions of the British system and we need to be protected from a prime minister seeking to accumulate American-style presidential powers," Dr Doig said.
Opposition Leader Peter Dutton said people wanted the Labor government to "move on and start dealing with issues that are more important".
Mr Morrison could face an inquiry by parliament's powerful privileges committee over the secret appointments.
Greens leader Adam Bandt has written to House of Representatives Speaker Milton Dick requesting the matter of whether the former prime minister misled parliament be examined by the committee.
A spokesman for Mr Dick told AAP he was considering the matter.
Mr Morrison has personally apologised to his former ministers.
He argued earlier in the week he had kept the roles confidential as he did not want to "undermine the confidence of ministers in the performance of their duties".
He said he only used the extra powers once, to block a gas drilling project off the NSW coast.
That decision, made in 2021, is the subject of a Federal Court appeal.
© AAP 2022