Fianna Fáil has launched plans to give every citizen a vote for the Seanad.
It has published a Bill which would allow every Irish passport holder - including those living abroad - a vote in Seanad elections.
It would also give votes to people in Northern Ireland who do not have a passport, but do qualify to be an Irish citizen.
The party says the role of the public in electing the Seanad can be expanded without needing to hold another referendum.
Last month the Taoiseach Enda Kenny ruled out giving votes to all citizens, or holding a referendum on the issue.
Party leader Micheál Martin says he will force a vote on the plans in the Dáil this term - and that this is an opportunity for change following the failed Seanad referendum campaign.