Geography, gender and ability will be key influencing factors for the coalition leaders in deciding the positions of some 17 junior ministers this week.
TDs who lost out on the chance at a senior post are being considered as strong contenders for a minister of state position.
Taoiseach Micheál Martin is expected to decide on the remainder of the 20 junior posts at a further Cabinet meeting. The roles of three, chief whip and two 'super' juniors, have already been allocated.
There is a possibility decisions on the roles may be put back further.
A top consideration is expected to be the need to appoint figures from the west, after the backlash over not appointing a TD to a senior role from a large part of that side of the island.
Fianna Fáil and Fine Gael will each get seven junior ministers while the Greens will take three.
Names linked with promotion in Fianna Fáil include Galway East TD Anne Rabbitte, Dublin West TD Jack Chambers and Meath East TD Thomas Byrne, all of whom negotiated the coalition deal for the party. Jim O'Callaghan is also tipped, after missing out on a senior role.
But long serving party TDs, such as Cork North-West's Micheal Moynihan, Limerick County's Niall Collins and Donegal's Charlie McConalogue could get the call up. Cavan-Monaghan's Niamh Smyth also looks likely to get some role.
One Fianna Fáil source said: “Martin will have to plug the hole in the West now. The women [TDs] were also mad at him on Saturday. The South East matters too.”
For Fine Gael, the choices are tough but less difficult. Leader Leo Varadkar is likely to also consider similar influencing factors.
Names touted as contenders include TDs Martin Heydon, current parliamentary party chairman, and Peter Burke, who have both played prominent roles during the pandemic. Former Education Minister Joe McHugh is also strongly tipped while TDs Damien English and Colm Brophy have been mentioned by party insiders as favourites.
“Varadkar will almost certainly want TDs who will definitely be running in the next general election,” said a party source.
This could mean that previous powerful ministers in the last government, including Charlie Flanagan, Richard Bruton, Michael Ring and Michael Creed, may not get the call up if there is any doubt at all about their political commitments after 2025.
Leo Varadkar is also strongly tipped to give junior roles to Kerry's Brendan Griffin and Dublin-Rathdown's Josepha Madigan.
Green leader Eamon Ryan will likely have the easier task of the three leaders. But it still requires difficult choices with just three junior posts to give out. TDs Ossian Smyth, Joe O'Brien, Brian Leddin or Marc O'Cathasaigh should get posts after performing well in the government formation negotiations.
But Malcolm Noonan is also strongly tipped particularly for his knowledge of community and rural affairs. Galway West senator Pauline O'Reilly could also leapfrog from the Upper House into a ministerial role, just as her colleague Pippa Hackett did.