A new law has been tabled so that the words 'Independent Alliance' can appear on election ballot papers.
The bill has been tabled by the alliance co-founder Shane Ross, who says the political system puts them at a disadvantage.
Ireland's current laws only allow ballot papers to be either blank, or carry the words 'non-party' - but don't allow the word 'independent'.
He also wants broadcasters to be allowed to carry party political broadcasts from independents, which are not currently allowed:
The Independent Alliance was formed in March of this year and comprises of TDs Shane Ross, Michael Fitzmaurice,Finian McGrath, John Halligan and Tom Fleming; and senators Feargal Quinn and Gerard Craughwell.