The High Court has thrown out the extraordinary argument by former senator Skye Kakoschke-Moore that she should be able to replace herself in the Upper House, after she resigned in the dual citizenship fiasco.

It paves the way for former Nick Xenophon Team (NXT) candidate Tim Storer to become South Australia's newest Senator, despite a bitter public feud with party founder Nick Xenophon.

Ms Kakoschke-Moore spent a little over a year in the Senate before resigning due to her mother's British citizenship.

Her lawyer David Jackson told the High Court that because she had now renounced her foreign links, she was no longer in breach of the constitution and should be eligible to be considered for the seat.

"There is no longer any section 44 impediment to Ms Kakoschke-Moore," he said.

"She remains a member of the Nick Xenophon Team.

"No other member of the Nick Xenophon Team has sought the Senate place vacated by Ms Kakoschke-Moore."

Other senators disqualified or forced to resign in the dual citizenship saga had been given the chance to argue the same position.

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Ms Kakoschke-Moore's lawyers said Mr Storer should not be considered because he had been expelled from the party, and his election would not accurately reflect the will of the voters.

"He has ceased to be a member of the political party for which South Australian voters voted in mid 2016," Mr Jackson told the court.

Mr Storer had lashed out at Mr Xenophon, who anointed his senior advisor Rex Patrick as his replacement in Canberra when he launched his South Australian state election campaign.

The Commonwealth had earlier described Ms Kakoschke-Moore's position as untenable and argued she be removed from the list of candidates.

The High Court threw out Ms Kakoschke-Moore's argument and ordered the count take place immediately, and Justice Geoffrey Nettle said that could be declared as early as Friday.

The likely result of that recount is that Mr Storer will be declared a senator for South Australia, and he could enter the red room as an independent.

But during campaigning in Adelaide, Mr Xenophon seemed to leave the door open for Mr Storer to return to the party.

"I think it's appropriate, once the dust has settled, to make it very clear that Tim will have every courtesy from us, whatever he needs should he want anything from us," Mr Xenophon said.

Court documents filed during the proceedings suggested Mr Storer was still disaffected with his former colleagues.

As the South Australian state election campaign ramps up ahead of the March 17 poll, the decision takes a vote away from NXT in the Senate.

"In the Senate, in terms of how the balance of power operates, two votes are still quite important in the scheme of things, in terms of a balance of power role," Mr Xenophon argued.

The only remaining citizenship case referred to the court is that of ACT Labor senator Katy Gallagher.

Ms Gallagher renounced her British Citizenship before nomination, but did not receive confirmation until more than a hundred days later, well after taking up her seat.

She has stood aside from the shadow cabinet while the High Court considers her eligibility, but insists she has legal advice that she took the required reasonable steps at the appropriate time.