The new Health Minister says he is positively considering a motion for a special committee to be set up to plan the future of the service.
A total of 89 deputies from all parties, with the exception of Fine Gael, have signed up to the idea.
It would hear proposals from experts and deliver a report within six months.
Minister Simon Harris said that the consensus on the issue is encouraging and he is committed to working with deputies to establish the body as soon as possible.
"It is extremely encouraging in the 32nd Dáil to see a consensus emerging on the health service," he stated.
"I have made it very clear that I want to see consensus on a 10-year plan for the health service and I am currently considering the motion with a view to encompassing thoughts and ideas of my own and reflecting the Programme for Government agreed with our Independent partners.
"I am committed to working positively with the opposition to make progress on establishing this committee as quickly as possible."