Some of Lucy Letby's baby victims' families say the investigation should have the ability to compel witnesses.
The nurse's conviction for the crimes at a Chester hospital prompted an independent probe on Friday.
However, attorneys representing two families argued this probe requires "real teeth" and should be mandatory.
The government claimed the investigation sought to learn.
After a 10-month trial, Letby was convicted guilty of killing seven newborns and trying to murder six at the Countess of Chester Hospital between 2015-16.
The jury acquitted her of two attempted murders and deadlocked on six others. She'll be sentenced Monday.
A separate investigation will investigate the neonatal nurse's killings and attempted deaths of the newborns.
The non-statutory inquiry's effectiveness in investigating the matter is disputed.