Independent TDs like Michael Healy-Rae and Shane Ross could be offered ministeries as part of a Fine Gael plan for a "rainbow minority government".
Acting Taoiseach Enda Kenny is to rapidly escalate attempts to form a new government that excludes Fianna Fail.
The Herald has learned that he intends to ask up to 20 Independents and the Green Party to play a role in writing a new programme for government.
The move will raise the stakes in the bidding war between Fine Gael and Fianna Fail as both parties seek to get enough support to justify a minority government.
Mr Kenny now wants to be in a position to appoint a Cabinet when the Dail meets on April 6.
"Independents thought we were looking for support on a case-by-case basis - but it's not, we want them in the room," said a source.
Party strategists accept they will fall short of the 79 seats necessary for a majority, but believe if they can get more than 65 votes, the pressure on Fianna Fail to allow the formation of a government would be too great.
Fine Gael sources described their new plan as a "modern version" of the 1948 coalition deal, which saw all parties except Fianna Fail enter a coalition. The Cabinet consisted of representatives from six parties and an Independent.
There are indications that the Independent Alliance; a group of five rural TDs; the Green Party; and a small number of standalone Independents - including Katherine Zappone and Maureen O'Sullivan -, are interested in taking talks to "the next level".
A key element of the Fine Gael plan involves convincing the Labour Party's seven TDs to abstain from voting against Mr Kenny on April 6.
Mr Kenny will ask his parliamentary party on Tuesday to allow him open "really substantial" negotiations that he hopes will ultimately lead to a programme for government.
Meanwhile, Fianna Fail is continuing talks with Independent TDs, and is due to give them a document on its plans for rural Ireland this weekend.
However, party strategists do accept they have huge ground to make up and will need somebody to publicly back them soon in order to gain some momentum.
In Brussels yesterday, Mr Kenny said people had voted "a different range of representation and I think, as the largest party in the Dail, it's important that we recognise what that range is.
"And that's why my responsibility continues to be to work with those groups and those individuals in understanding what their concerns are, and what mandate they brought with them from their people, being properly elected to the Dail, and to reflect that in issues that can be dealt with by the next government," he said.