Independent TDs are now just one short of the number needed to form an official group in the Dáil, which could make them a powerful voice on the opposition benches.
Since Tuesday, Dublin Central TD Mr Tony Gregory has led efforts to bring the Independents into a cohesive group entitled to full speaking rights and other privileges.
The latest boost to the Independents came following Wednesday's decision by the Wicklow Independent, Ms Mildred Fox, who supported Fianna Fáil and the Progressive Democrats over the last five years, to join them.
The formation of an Independents group will cause difficulties for both the Greens and Sinn Féin, both of which had hoped to lead the opposition deputies bar Fine Gael and Labour.
Under the Oireachtas's current standing orders, 13 of the 25 Independents, Greens and Sinn Féin TDs must come together before they will be recognised as a technical group.
Following Ms Fox's agreement, the Independents now need either Donegal North East TD Mr Niall Blaney or Kerry South's Mr Jackie Healy-Rae to come on board before the Dáil resumes next Thursday.
According to sources, Mr Blaney has said he will "reflect" on the matter over the weekend, while Mr Healy-Rae, who is watching to see the outcome of Fianna Fáil's talks with the Progressive Democrats, is being a little more reserved.
The efforts to create a group began with a meeting between Mr Gregory, Independent Health Alliance TD Mr Finian McGrath and Tipperary South TD Mr Seamus Healy, followed quickly by the arrival of Sligo-Leitrim's Ms Marian Harkin.
Last night, Mr Gregory rejected suggestions that the Independents were trying to "freeze out" Sinn Féin or the Greens and said they had not considered whether they would invite them if they already have 13 TDs.
"I would be very anxious to see the Dáil's standing orders changed. I have been a victim of them for long enough. The Greens should have full rights, so too should Sinn Féin," he told The Irish Times.
Membership of a technical group does not imply agreement on policy - it is simply a way of exercising greater influence in the Dáil using Private Members Time, priority questions to ministers and by getting more committee places.
Meanwhile, the battle for the Fine Gael leadership between the three declared candidates, Carlow- Kilkenny's Mr Phil Hogan, Dublin North Central's Mr Richard Bruton and Mayo's Mr Enda Kenny continued yesterday.
Following discussions yesterday, the three have agreed not to create divisions within the party by seeking the support of constituency organisations or by divisive public declarations.
Efforts to find a consensus leader failed after a straw poll among 38 of the 49 members of Fine Gael's parliamentary party showed no clear favourite.