Sinn Féin remain hopeful they can remain ahead of Fine Gael to claim the final European seat in Ireland South.
While just one seat has been filled in the 12-county constituency by Fine Gael's Sean Kelly, it is expected that both Fianna Fáil's Billy Kelleher and Independents4Change candidate Mick Wallace will be elected in the coming counts.
Based on the current numbers after 15 counts and expected transfers, Green Party senator Grace O'Sullivan is on track to take the fourth seat.
It is then expected that the two out-going MEPs left in the race, Deirdre Clune and Liadh Ní Riada will be locked in a tussle for the final 'cold storage' seat which cannot be taken up until Britain leaves the EU.
Counters are currently redistributing the votes of Labour's Sheila Nunan and Fine Gael's Andrew Doyle, which should give Ms Clune a boost.
Speaking at the count centre in Nemo Rangers GAA club, Sinn Féin TD Jonathan O'Brien said: "Obviously Deirdre is picking up a lot of transfers here, it's going to bring her back into contention.
"I am not confident that she is going to overtake Liadh at this stage, so Liadh could still be in fourth after this count and it will probably come down to Malcolm Byrne's elimination later on and we will see where we are going from there.
"I still think we are in a very strong position, we are in fourth, we have stayed in fourth since the count opened," the Cork North-Central TD said.
Asked if the party would be disappointed if Ms Ní Riada ends up taking the fifth seat he said: "A seat is a seat, we set out to win a seat. If it's the fifth seat obviously we will need to analyse the impact that has because nobody is exactly sure what the fifth seat entails yet," he said.
The race for seats in Ireland South has heated up as Labour candidate Shelia Nunan and Fine Gael's Andrew Doyle have both been eliminated in the 15th count.
Mick Wallace, who has been mopping up significant transfers, gained 5,545 votes from the distribution of Solidarity PBP candidate Adrienne Wallace's votes. If he continues on this track he could be elected in the next count when Ms Nunan's and Mr Doyle's votes are distributed. This would see him pip Fianna Fáil's Billy Kelleher for the second seat in Europe.
The counting of votes in the next round is now expected to take several hours, but the two eliminations will speed the process up.
Poll-topper Sean Kelly was re-elected to the European Parliament yesterday afternoon. However the race is still tight to fill the remaining four seats, the last of which will not be filled until Britain leaves the EU.
Currently Indepdentes4Change TD Mr Wallace is leading the pack with 95,780 followed by Mr Kelleher on 89,036 votes.
Sinn Féin's Liadh Ní Riada currently has 87,322 votes, Green Party candidate Grace O'Sullivan has 84,741 votes while outgoing Fine Gael MEP Deirdre Clune is on 69,560.
However, Ms Clune is expected to gain significant transfers from party colleague Mr Doyle.
Earlier: Green Party's Saoirse McHugh eliminated on eleventh count
The Greens' star candidate in the European elections, Saoirse McHugh, has lost her chance at becoming an MEP after being eliminated in the midlands north west count in the early hours of this morning.
Ms McHugh's election race was ended on the eleventh count in the sprawling constituency, which is expected to fill its three remaining seats throughout today.
Despite being predicted to win 12% in the RTE-TG4-Red C exit poll after Friday's European election vote, the 28-year-old from Achill Island in Co Mayo fell short of this target.
As such, she was always facing an uphill battle to claim one of four seats in the increasingly competitive constituency, a hope that ended just after 1am this morning.
In the eleventh count in the constituency - which will start its twelfth count at 10am today before a likely twelfth count announcement at lunch time, and which has to date only elected Fine Gael's Mairead McGuinness:
- Luke 'Ming' Flanagan, Ind, received (+2,966) 97,319
- Matt Carthy, Sinn Féin, (+974) 84,825
- Maria Walsh, Fine Gael, (+4,282) 80,338
- Peter Casey, Independent, (+1,875) 66,555
- Brendan Smith, Fianna Fáil, (+17,712) 64,532
- and Saoirse McHugh, Greens, (+1,179) 61,957
Non transfers: 5,622 (total of 20,405).
The result meant Ms McHugh was eliminated on the eleventh count, with her votes due to be distributed in the twelfth count today.
Ms McHugh had been consoled by Greens leader Eamon Ryan on Monday after it became apparent the eventual outcome was likely to come to pass.
Speaking to reporters on Monday, Mr Ryan applauded Ms McHugh's debut political performance, saying she has "inspired" the entire country to think green.
"You're always very careful on the result, I think it will be tough because she may not quite have the votes to be in the race.
"But you don't know, we'll have to wait and see what the count is.
The exit poll probably exaggerated our vote, but come what may she has done a terrific job.she was a brilliant candidate for us.affected the green wave across the country, people were inspired by her.
"And I think she's done a remarkable job.
"I haven't had a chance to talk to her, I want a chance to sit down and have a good chat with her, but I always felt when I met her first how do we get people to wake up to the change we have to make, and she was kind of bemoaning the fact everyone else is talking about it but not actually doing it.
"And eventually I said well Saoirse you should run because you know if others aren't doing it well then you should stand up and be one of the decision makers.
"So I think she did brilliantly, and it wasn't just the television debate," he said on Monday.
Presidential race runner-up Peter Casey and Fianna Fáil TD Brendan Smith are locked in a neck and neck battle to overtake each other in midlands north west in a duel which could have wide-reaching implications for the European elections race.
After the eleventh count in the sprawling constituency was announced, Mr Casey was surprisingly still ahead of Mr Smith.
And, while both candidates are off the pace, the complex nature of vote transfers means unless Mr Smith can overtake his rival in the next count, Fianna Fáil transfers could push Mr Casey back into real contention for a seat.
With eleven counts completed, midlands north west has still only filled one of four available seats, with four-time Fine Gael MEP Mairead McGuinness cruising home on the first count with 34,630 votes - the highest first preference vote in the country and 15,644 votes more than the 118,986 election quota.
She is set to be followed by Independent MEP Luke 'Ming' Flanagan (97,319) by the announcement of the twelfth count at lunchtime today, which is likely to see Mr Flanagan benefit substantially from the distribution of Saoirse McHugh's 61,967 votes.
However, the race for the final two seats is increasingly gaining more interest, with a number of unexpected vote transfer twists potentially pushing Mr Casey back into contention.
This is because Mr Casey is now on 66,555 votes, still above Mr Smith on 64,532 votes even after Fianna Fáil TD Anne Rabbitte's vote was distributed at the eleventh count.
If he can remain above Mr Smith after Ms McHugh's vote is distributed in the twelfth count today, Mr Casey claims he will benefit from a Fianna Fáil transfer bump when Mr Smith is subsequently eliminated.
If this happens - an issue which will remain up in the air until the twelfth count announcement - he could potentially catch either Fine Gael candidate Maria Walsh (80,388) or Sinn Féin MEP Matt Carthy (84,825).
And, while the possibility remains more unlikely than likely, the sub-plot is increasingly gaining attention in the count centre, with the three candidates vying for just two seats deep into the contest.
The midlands north west European elections count will resume at 10am this morning, with a twelfth count announcement likely by lunchtime.
It is expected the counts marathon will conclude tonight.
We should get a clearer picture of who will be elected to represent Ireland South in the European Parliament later today.
14 counts down and so far, only Fine Gael's Sean Kelly has been elected.
But today, we will get the best indication yet of who will take the other four seats.
After a big boost from transfers yesterday, independent Mick Wallace is in a strong position:
Fianna Fáil's Billy Kelleher is just behind him and looks to be in with a very strong chance.
Then it appears to be a race between Fine Gael's Deirdre Clune, the Green Party's Grace O'Sullivan and Sinn Féin's Liadh Ní Riada for the last seat.
Grace O'Sullivan has done well from transfers in the last few counts and she will be hoping that continues when Labour's Sheila Nunan goes out.
For Deirdre Clune, fellow Fine Gael candidate Andrew Doyle's elimination will be crucial if she is to be in with a shot.
Where the transfers go today will be a big indicator of who will be going to Brussels.
Meanwhile last night, independents4change Clare Daly leap-frogged Fianna Fáil's Barry Andrews into third place in Dublin.
Andrews will now have to wait to go to Brussels, because Dublin's fourth seat does not become operational until the UK leaves the EU.
The Green Party's Ciarán Cuffe topped the poll in the capital, followed by former Tánaiste Frances Fitzgerald.