Labor senator Katy Gallagher's eligibility to sit in parliament is likely to be tested by the High Court after the Greens decided they were inclined to support any government referral.
The Greens' party room on Tuesday agreed to support "bona fide referrals" but not any partisan warfare.
However, the minor party wants to wait until the family histories and citizenships of lower MPs are published.
The Greens' decision comes after Opposition Leader Bill Shorten said Labor would work with the Turnbull government to decide which MPs should be referred to the High Court.
"Let's get all the disclosures in, I think that's the sensible sequence of events, and we will sit down with the government and endeavour to resolve the citizenship controversy," he told reporters in Canberra on Tuesday.
"When we've got all the facts on the table from both sides then we'll work through this in a bipartisan fashion."
Senators produced their citizenship details on Monday while lower house MPs had until Tuesday morning to do likewise.
The government is weighing up whether to seek Senate support to refer Senator Gallagher to the High Court, making her the first Labor parliamentarian to face scrutiny in the fiasco that has claimed the scalps of nine parliamentarians so far.
Senator Gallagher, the former ACT chief minister, did not receive confirmation of her UK citizenship renunciation until two months after nominations closed for the 2016 federal election and 118 days after she lodged the application.
Under section 44 of the constitution, dual citizens are ineligible to sit in parliament.
She has legal advice which says she took all of the steps required of her under British law to renounce her UK citizenship.
Junior minister Michael Sukkar says it is clear Senator Gallagher was a dual citizen when she took up her Senate seat.
"She has got to go. She should go today," he told Sky News.
Labor MPs Susan Lamb and Justine Keay and independent Rebekha Sharkie are also in the government's sights for similar scenarios.
But Labor continues to argue the difference between the cases of its MPs and those found ineligible by the High Court is "night and day".
"Barnaby Joyce, Fiona Nash and the others that were referred to the High Court took no steps to renounce their dual citizenship," deputy Labor leader Tanya Plibersek told reporters in Canberra on Tuesday.
"We are confident that Labor MPs have taken all reasonable steps to renounce any dual citizenships."
