Back in July, a court agreed and appointed a financial guardian for the children. But a state appeals court quickly issued a temporary stay on that order.
Peterson and Allred say Suleman has exploited her octuplets for financial gain. She has countered that the two are suing just to promote themselves.
In court, Suleman's attorney argued that the group has no legal standing to get involved in the family's affairs. He called it a power play by Allred.
"The legal issue before the court today involves the question of whether or not Paul Peterson, our client who has been a strong and persistent advocate for more than 20 years for the rights of child performers, would have the legal right to pursue the petition. The legal question was does he have 'standing'?" said Allred.
"A third party that reads a newspaper just can't run into court and try to, and try to take away a parent's parental rights. It's a very intrusive, invasive remedy to run into court to try to keep a parent from making decisions about their children," said Art LaCilento, Suleman's attorney.
Sulman was not in court Thursday.
The judge did not make a ruling Thursday. He said he will look at all the statements and make a decision Friday, which will be posted on the court's Web site by noon.
A reality show about Suleman and the octuplets is scheduled to start shooting next month.