Fine Gael members will have more power to stop the party from going into government, under plans to be considered at its Ard Fheis.
Under the proposal, TDs and Senators would have half of the say when Fine Gael is considering Government arrangements with the rest of the vote in the hands of other members.
It comes as talks between Fine Gael and Fianna Fáil on the future of the confidence and supply deal continue.
Fine Gael's Ard Fheis takes place over the next two days at the CityWest Hotel in Dublin, with Taoiseach Leo Varadkar to give an address tomorrow evening.
The party says extending the Confidence and Supply Agreement until the Summer of 2020 is badly needed for stability around Brexit.
The party's Ard Fheis will follow a day-long meeting between Fine Gael and Fianna Fáil negotiating teams on what happens when the deal runs out.
Fine Gael Party Chairman Martin Heydon says Brexit will be high on the agenda across the weekend:
Mr Heydon said: "It will be one of our biggest attendances at an Ard Fheis, with in excess of 2,500 people expected to attend.
"We will look to discuss a whole range of issues from forging new alliances in a post-Brexit Europe, using our role at the heart of the influential European People's Party which has been important to our negotiations in Brexit as well as forging a new relationship with the UK and US."
