A group of independent TDs now has 12 members, just one short of the number needed to form an official group in the Dáil. If successful in their bid to form the group, the independents will have access to speaking time and other privileges.
Sources close to the group said Wicklow TD, Mildred Fox, had joined them, and that they were trying to contact the last two Independents, Niall Blaney and Jackie Healy Rae.
Under Dáil rules, a party is only recognised as an official group if it has seven or more members.
However, deputies outside the officially recognised parties can form what's known as a technical group to obtain access to speaking time and other benefits, if it includes a majority of TDs not in the main groups.
If the Independents do succeed in forming a group, it will have more Dáil speaking time than either the Greens or Sinn Féin, although those parties say they are continuing talks in an effort to form a technical group themselves.
Membership of a technical group does not imply agreement on policy - it is simply a way of exercising greater influence in the Dáil.