A Families Commission report on gay and lesbian parenting recommends birth certificates allow for more than two parents to be listed.
Many of the 19 families interviewed for the study were worried about the lack of security they have if things go wrong.
The report's co-author, Alex Gunn, says the study's participants did not find the law helpful or secure.
Dr Gunn, an education lecturer at the University of Canterbury, says though private contracts can be drawn up, under current laws the parents who are more involved with the child will usually get custody.
She says allowing all parents to be on the birth certificate would ensure the child's inheritance rights.
But national director of the Family First organisation, Bob McCoskrie, says the report avoids asking what is best for the child.
Mr McCoskrie says allowing "teams" of parents could leading to some worrying social engineering.