State Senator Mark Leno (D-San Francisco) wrote the bill that would allow judges to recognize multiple parents in cases where children would be best served by several parental relationships. All parents would still be required to meet existing standards for legal parenthood.
Leno said the bill is a response to the evolving nature of America's families.
Supporters cited several examples where the law could be applied, including a lesbian couple that conceived a child with the help of a sperm donor who has been involved as a parent, or a man who married a woman while she was pregnant with another man's child, who also maintained his role a father.
They also say the bill could keep some children out of foster care by establishing additional parents with caretaking and financial responsibility.
Opponents fear there could be no limit to the number of parents a child could have. They also say Leno's bill could undermine conservative family values.
Pennsylvania, Maine and several other states recognize more than two parents.
Supporters say it is unlikely the number of parents would proliferate because the bill does not change the definition of parenthood or allow temporary caretakers such as boyfriends or girlfriends to be considered as parents.
Instead, SB1476 involves families in which more than two adults take a child into their home and present the child as their own, not as a step-child.
Backers dismissed moral concerns, saying the bill is a simple modernization of family law.
The Associated Press contributed to this report.