Labor wants more coalition MPs to "ventilate their feelings" about Home Affairs Minister Peter Dutton's eligibility to be in parliament before trying again to have him referred him to the High Court.
Mr Dutton is facing questions about his eligibility to sit in parliament due to his family financial interest in two childcare centres.
Labor leader Bill Shorten says the opposition will wait until it knows it has the support of some government MPs to try to refer Mr Dutton.
"We have to, of course, wait until there is a majority to refer the matter," he told ABC TV on Sunday.
Julie Bishop this week called for "clarity" over Mr Dutton's eligibility and backed former prime minister Malcolm Turnbull's calls for his referral.
Mr Shorten believes there could be others like her.
"She shouldn't have to carry the can for the whole of the Liberal Party, as she's had to. I think there's other MPs," he said.
"We need to just see government MPs perhaps ventilate their feelings a little more in the course of the week."
An earlier Labor motion for a referral was defeated by just one vote on August 23.
Section 44 of the Constitution disqualifies anyone who has a "direct or indirect pecuniary interest" in any agreement with the Commonwealth.
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At the height of the Liberal leadership crisis, Solicitor General Stephen Donaghue advised that he could not categorically determine Mr Dutton's status and only the High Court could.
Mr Dutton told parliament on Thursday the advice he has taken in relation to his position has "put the question beyond doubt".
But constitutional law expert Anne Twomey told The Australian on Saturday that the Solicitor-General's opinion brought up information that "raised considerably the risk of disqualification".
Crossbenchers Cathy McGowan and Rebekha Sharkie have suggested they would vote for a referral.
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