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Brad Pitt and Angelina Jolie are in the midst of a complicated legal battle for custody of their six children. Now, legal experts say, their next moves will be key — and so will where the wrangling will play out.

The Los Angeles Department of Children and Family Services (DCFS) had been investigating the family following allegations Pitt was verbally and physically abusive towards their son Maddox. But on Wednesday, sources confirmed that DCFS concluded the investigation with no findings of abuse.

L.A.-based family law specialist Steve Mindel — who does not represent Pitt or Jolie – told PEOPLE that while the case will likely now be referred back to family court, it doesn’t have to remain there.

“The parties have to make a decision as to whether they’re going to pursue this in the public court system or whether or not they’re going to go to an alternative dispute resolution — either mediation, arbitration or a private judge program,” he says.

Brad Pitt Angelina jolie
Credit: Charley Gallay/Getty

Where Pitt, 52, and Jolie, 41, decide to go next depends on what level of privacy they are seeking, he explained. Most court proceedings are public — while mediation is highly confidential and allows Pitt and Jolie to mutually agree to decisions.

“One would think given Angelina and Brad’s privacy, their six children and the fact that they all have to live through all of the stuff that’s going to be published about this, they would want to do it in one of the more private settings,” Mindel says.

May 8, 2014 - London, England, United Kingdom - BRAD PITT and ANGELINA JOLIE arrives for the ''Maleficent'' costume display opening at Kensington Palace on May 8, 2014. (Credit Image: © Ash Knotek/Snappers/
Ash Knotek/Snappers/

Still, there’s lots to resolve, and Pitt has made it clear he plans to push for more access to his kids. He filed a response to Jolie‘s divorce petition on Nov. 4 and asked to share joint physical and legal custody of Maddox, 15, Pax, 12, Zahara, 11, Shiloh, 10, and 8-year-old twins Knox and Vivienne. Jolie has requested sole physical custody, with visitation for Pitt.

Per a temporary recommendation by DCFS, for the past several weeks, the children have been living with Jolie, with supervised visitation for Pitt. But Pitt “has been very unhappy with the arrangement,” a source tells PEOPLE in the new issue. “He loves his kids and wants to spend more time with them.”

Pitt could seek to change that agreement now that the DCFS investigation is over, but L.A.-based criminal defense attorney Alaleh Kamran, who’s also not involved with the case, thinks Pitt will continue go by the terms of the voluntary agreement “as a gesture to keep peace between the parties.”

Mindel agreed — saying the supervisor could fuel a positive case for Pitt if called to testify. “This person is a therapeutic monitor,” Mindel said. “This person could be very helpful to Brad in future litigation. You have to anticipate that if Brad is a good parent, he might want to have the monitor in place for another few weeks so he can develop more evidence about what good parenting skills he has.”

“He is going to want that to support his position because otherwise, it’s his word against Angelina’s word reporting to her what the children tell her,” Mindel furthered. “Having the therapeutic monitor in place is very helpful to Brad.”

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If Pitt no longer agrees to supervised visits, he and Jolie would have to both agree on next steps — or begin proceedings in court, Mindel says. But either way, both legal experts say the DCFS ruling plays favorably for Pitt and can strengthen his case for joint custody.

“There is no difference between them anymore — it’s a 50/50 stake,” says Kamran. “He’s the father. He gets everything the mother does… Because there are no clouds hanging over him, he’s just as entitled [to access to his children] as any other parent.”

• Reporting by KARA WARNER