Independent Ireland's Michael Fitzmaurice has said that his party would consider going into a coalition government with Fianna Fáil and Fine Gael.
"We have made it very clear that we're not here to just rock up to Dublin; we're here to sit down with any of the main party's," said Mr Fitzmaurice, who was deemed elected following the first count in Roscommon-Galway.
"We are pro-agriculture, we are pro-housing and we are pro-balanced regional development. I think a lot of the stuff we had on our document the two main party's took our clothes over the last few weeks.
"We are prepared to sit down and talk. We look to have four (seats) in the bag.
"I think we're looking pretty good in Sligo and in Galway West. I know that there's a recheck in Galway East but Declan Geraghty is in with a real shout for the last seat.
"There's a possibly of seven seats but there are three of them up in the air at the moment," he said.
Many smaller parties and Independents are hoping to make gains in the election.
Earlier, Independent Ireland leader Michael Collins said they were "looking good" to hold on to their three seats and could be in a position to double that number in this election.
Labour was also in contention to win extra seats, with the party believing it is in a position to pick up TDs in Dublin Fingal West and Dublin South-West.
The party's leader Ivana Back has said that her party has seen "really strong results".
Verona Murphy was the first Independent candidate elected to the 34th Dáil, topping the poll in Wexford following the first count.
Aontú leader Peadar Tóibín has retained his seat in Meath West after he was elected on the fourth count.
'I'm still hopeful,' says Boyd-Barrett
Richard Boyd Barrett, People Before Profit-Solidarity, said that nationally his party's percentage is up, but they are still struggling in a few areas "and it's not clear how that is going to go".
"I'm still hopeful," he said.
He said he was positive about his position as well as Paul Murphy and Ruth Coppinger, adding that Hazel de Nortúin was in "very strong contention".
Mr Boyd Barrett retained his seat in the Dún Laoghaire constituency following the seventh count.
However, he said Gino Kenny (Dublin Mid-West) and Mick Barry (cork North-Central) had a fight on their hands.
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