A fund has been established to help pay for any gaps in his care, whether it be for experimental medications, or assistance getting around.
His parents on Friday said there were some hopeful signs in his condition.
"His status changes constantly," said his step-father Mark McGowan of Petaluma, adding he is able to breathe on his own. He also has some feeling in his arms.
"They're focusing on getting motor skills in his arms improved. He doesn't have a lot of movement in his hands and fingers," said McGowan.
He was at Cox's side in the intensive care unit of Renown Regional Medical Center in Reno, along with other family members.
Cox's mother, Maureen McGowan, said he was "sitting up" and able to eat. Doctors said he would probably be able to go directly to Kaiser's spinal care rehabilitation facility in Vallejo next week and avoid transfer to another acute care facility first.
Cox, 18, was vacationing with friends Tuesday when he dove into shallow water at a South Lake Tahoe beach and broke his neck.
The accident left him paralyzed from the chest down.
The fund for his rehabilitation will go toward expenses that may not be covered by his Kaiser health plan.
"We know there are going to be rehab expenses coming up that insurance is not going to cover," said Mark McGowan.