The main political parties have agreed to consider proposals over the summer for Dáil reform in the hope of agreeing a package of changes in the autumn.
Government chief whip Tom Kitt last night met whips from Labour, Fine Gael and the technical group - consisting of Independents, the Green Party and Sinn Féin - to discuss the reform.
This follows last week's Opposition objections to proposals put forward by the Government which the Opposition said would reduce the demand on the Taoiseach to be accountable to the Dáil.
Labour Party whip Emmet Stagg described last night's meeting as "positive".
It was attended by Mr Kitt, Mr Stagg, Fine Gael's whip Paul Kehoe and the technical group whip Tony Gregory.
Both Fine Gael and Labour put forward alternative proposals to those of the Government.
Several more meetings are expected to consider these, as well as re-examining proposals produced when Seamus Brennan was government whip in the 1997-2002 coalition.
The Government yesterday made it clear it was open to trying to agree changes in Dáil procedures. Government sources said while they believed their proposed reforms would be good for the operation of the Dáil, they would not seek to force them through in the face of Opposition objections.
The Government's proposals would ensure that the Taoiseach has prior notice of questions to be raised during Leaders' Questions.
They would also see the Government chief whip rather than the Taoiseach taking the Order of Business in the Dáil.
Labour's alternative proposals would see more sitting days, longer working hours and shorter holidays.
They include having the Dáil meet four days a week instead of the usual three, a summer recess of six weeks instead of the usual 12, and significantly-reduced breaks at Christmas and Easter. The practice of taking a full week off at St Patrick's Day and Hallowe'en would be abandoned.
It wants the Order of Business to be reformed to allow urgent and topical matters to be raised by TDs. Question time to Ministers should be extended, television and radio coverage of the Dáil should be enhanced and Oireachtas proceedings should be available live on the internet.
It has also called for a Committee of Investigations, Oversight and Petitions to receive petitions from groups seeking any redress of grievances connected with public services and public administration.
An Office of Parliamentary Investigator should be set up "to ensure timely and cost-effective investigation of issues giving rise to significant public concern". All tribunals should be televised.
Legislation should be introduced to ensure the doctrine of Cabinet confidentiality "cannot be used to cover up necessary investigations".