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What people don’t realize is “that even in stepfamilies or open-adoption scenarios, children still have at most two legal parents,” Ms. Marquardt wrote. “When it comes to legal parenthood, this ‘rule of two’ has not been breached.”

The “rule of two” is currently the law in California, which is why Mr. Leno introduced a bill this year that would explicitly permit judges to find that a child had more than two parents.

“The definition of family is evolving,” the openly gay lawmaker said. “All this bill does is give authority to a court [to use] when it’s required to protect the best interest of the child.”

Courts need this freedom to recognize all the parents in a child’s life, and have the authority to assign custody, visitation and child support among all the parents, said the National Center for Lesbian Rights, one of the co-sponsors of SB 1476.

Two family law organizations, while agreeing with the concept of multiple parents, objected to aspects of the bill and urged Mr. Brown to veto it.

If it is reintroduced, “a lot of people will be happy to work on this,” said Diane Wasznicky, president of the Association of Certified Family Law Specialists. The California chapter of the Association of Family and Conciliation Courts also objected, she said.

But others saw a “Pandora’s box of conflicting laws and legal contracts,” as Brad Dacus of Pacific Justice Institute put it.

“This gives a lot discretion to the family law judge for whatever they judge to be in the best interests of a child. That’s a lot of power,” said Jennifer Roback Morse, founding president of the Ruth Institute, a project of the National Organization for Marriage.