Backbench MPs from both major parties have publicly backed calls for an audit of every politicians' background to detect any more dual citizenship breaches.
It came as the Coalition sweated on advice from the UK Home Office on the potential dual citizenship of Senate President Stephen Parry.
Labor has again rejected an audit despite calls from within the party to do it.
"We're very confident no Labor MP is a dual citizen. We have got strict processes and careful procedures when people are applying to be candidates," Acting Labor Leader Tanya Plibersek told reporters on Wednesday.
"The simplest way of addressing this is for every member of Parliament and candidate to follow the rules."
Labor's position hasn't changed since the citizenship scandal which engulfed seven politicians began earlier in the year.
But one backbencher has publicly backed calls for an audit.
"We need to know, we need to be sure everyone's there and they have eligibility," Labor MP Meryl Swanson told the ABC on Wednesday.
"There can't be one rule, instituted by the High Court no less, for some [and] others just mopping their brow thinking 'Phew, we dodged that".'
Politicians are floating various options about how an audit could be carried out.
Liberal backbencher Craig Kelly backed an investigation by the Australian Electoral Commission.
"There's virtually an informal audit being done by the media, which is like a death of a thousand cuts," he told the ABC.
Nationals MP Llew O'Brien also told the ABC he "wouldn't have an issue" with an audit if the public wanted it.
The Greens said it would support any model which was independent of Parliament but had the support of the major parties.
"After an audit, what we'd end up with is question marks, I suspect, over a handful of MPs," he said.
"We know some of them are eligible for dual citizenship and they haven't provided proof they've renounced that dual citizenship."
'Business of government will go on': Julie Bishop
The Acting Prime Minister reiterated the government still holds a majority in the Lower House of Parliament as it faces another embarrassing turn in the citizenship saga.
The Senate President Stephen Parry is waiting to hear back from the UK Home Office about his possible British citizenship through his father.
If it's confirmed, he has signaled he will resign and will become the first Liberal casualty of the saga which recently ensnared seven other politicians.
"The business of the government will go on," Ms Bishop told Channel Seven on Wednesday.
"I'd rather we didn't have to face these challenges but we do, and we will deal with them."
But she did not absolve Senator Parry for his oversight in not clearing his status sooner.
"Each member and senator has a responsibility to ensure that they are eligible to stand for Parliament," she said.
"In the case of senators found in eligible, they will be replaced in an established process of either a casual vacancy or recount at the last election."
The Attorney-General said yesterday it was unlikely there were any more Liberals with potential dual citizenships.
"Nobody else has come forward and I've not seen any evidence that any other member of Parliament has this problem," George Brandis said in a press conference on Tuesday.
"It's not yet clearly established that Senator Parry is disqualified."
If Senator Parry does resign, he would create a casual vacancy for his Senate seat which would be filled by the next person on the Liberal Party's Tasmanian Senate ticket.
Former Tourism Minister Richard Colbeck has told SBS News he would contest the seat if there was a recount.
The Prime Minister and Opposition Leader are yet to warm to the idea of an audit.
In August, Prime Minister Malcolm Turnbull deferred questions on whether a citizenship audit was needed because the High Court was set to consider the fates of seven politicians over their dual citizenships.
"I think we should await the High Court's deliberations," he said in a press conference.
"The law will undoubtedly be clarified after their decision."
In August, as speculation around the possible Ecuadorian citizenship of Labor Senator Katy Gallagher peaked, Bill Shorten would not commit to an audit.
"We've done nothing wrong," he told reporters in the Queensland town of Bundaberg.
"Just because the Deputy Prime Minister, and just because Senator Canavan and just because Minister Nash haven't got it right, doesn't mean everyone else is automatically either a suspect or done something wrong."
