The inquiry will have 12 months to investigate Grace's care
A final vote on the terms of reference for the 'Grace' inquiry has been deferred until Wednesday.
TDs are being given more time to consider the plans, but the inquiry could be set up before the end of the week.
However several TDs have hit out at the fact that other residents in the same abusive foster same will have to wait for their own inquiry.
Labour leader Brendan Howlin says the government is ignoring the calls the man hired by the HSE to review the case:
"Outside of the Grace case, the only capacity that we are giving this inquiry is to scope out a potential further inquiry - and that is it.
"It can carry out the scoping exercise, and that is it - it can do no more.
"And that is hugely different from what Conor Dignam wanted", he added.
Senior counsel Marjorie Farrelly, a barrister based in Cork, will be given 12 months to investigate the circumstances of Grace's care.
The Commission of Investigation is designed to establish exactly how Grace was left with her foster family in the first place, what monitoring there was of her placement, and the decisions made about how she was left there.
It will also investigate the extent to which there may have been abuse, irrespective of who might have carried it out.
There will be a particular focus on the decision made in 1996 to remove her, and why it was not followed up.
The foster family lobbied the then-health minister Michael Noonan, and the inquiry will examine whether what followed was normal practice or whether it constituted an intervention on his part.
Junior Minister Finian McGrath said earlier no stone would be left unturned by the inquiry.
"All of those areas will be covered, all of those questions will be answered and they'll be dealt with in a comprehensive manner.
"There'll be no question of any cover-up, and all those kind of allegations will be dealt with by Marjorie Farrelly and the Commission of Inquiry.
"Because these families deserve the truth, deserve to know the facts - but more importantly at the end of the process, they need to know that action is going to be taken".
In an RTÉ interview broadcast on Monday, the mother of Grace said she cannot accept an apology from the Health Service Executive (HSE).