Independents Michael McDowell, Ronan Mullen and Alice Mary Higgins have all been re-elected to the Seanad.
Mr McDowell was the first to be elected in the National University of Ireland (NUI) panel, with 11,390 first preference votes.
Seanad Eireann is the upper house of the Irish parliament.
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Out of a valid poll of 36,114, the NUI panel had a quota of 9,029.
Speaking afterwards, Mr McDowell said he was “very grateful” to be re-elected and returning to the 27th Seanad.
Outgoing senators Ronan Mullen and Alice Mary Higgins were re-elected on the eighth count.
It means that all three candidates on the NUI panel have held their seats.
On the Dublin University/Trinity College panel, incumbent Lynn Ruane topped the poll with 3,761 votes, and was elected on the 11th count.
Former children’s minister Katherine Zappone, who was among the most well-known of the candidates, was eliminated on the ninth count.
Meanwhile, the counting process for the five vocational panels is continuing at Leinster House.
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A total of 111 candidates are competing for the 43 seats.
Counting began with the Cultural and Education panel on Thursday, and is expected to continue until Bank Holiday Monday.
As soon as each panel is counted, the counting staff will move to the next panel.
Counting will begin at 9.30am each day and continue until around midnight.
All results will be posted on the Oireachtas website and social media sites.
The counting order of panels will be Cultural and Education; Agricultural; Labour; Industrial and Commercial; and Administrative.
The vast majority of the public do not have a vote in the Seanad.
The Dail’s TDs, outgoing senators and local authority councillors make up the electorate for the five vocational panels.
Counting in the Seanad elections continues at the RDS in Dublin (Brian Lawless/PA)
Graduates of NUI institutions and Trinity College Dublin vote for the six seats across the two panels.
The final 11 Seanad seats are appointed by Taoiseach Micheal Martin.
Among those running for a seat are Fine Gael’s Alan Farrell, Fianna Fail’s Joe Flaherty, Green Party’s Malcolm Noonan, as well as Sinn Fein’s Conor Murphy and Pauline Tully.
Mr Murphy, who is the party’s chief negotiator and Stormont Economy Minister, announced the surprise move last month.
The Newry and Armagh representative, who is running in the Industrial and Commercial panel, said that “constitutional change is coming” and that his experience “will drive efforts for referenda and Irish reunification”.
Other notable candidates include Frances Black, Restaurants Association of Ireland chief executive Adrian Cummins, and former TD Cathal Berry.
Elected senators will debate legislation put forward by the Government.
They can amend Bills and propose their own Bills but cannot prevent one from becoming law.