Last month Stow's doctors upgraded his condition from critical to serious after being a coma since a March 31 attack outside of Dodgers Stadium in Los Angeles.
The family wrote on their website for Stow, a 42-year-old Santa Cruz father of two who worked as an emergency medical technician in Santa Clara County, that his fever has been down since Wednesday and he does not have any infections.
With these improvements, the family said they hope Stow can receive a shunt in his brain.
"We have heard from many people that this could, while eliminating excess fluid, help with his responsiveness," family members wrote.
San Francisco General Hospital spokeswoman Rachael Kagan said Stow remains in serious condition at the hospital under the care of neurosurgeon Dr. Geoff Manley.
Stow has been receiving treatment at San Francisco General Hospital since transferring from a Los Angeles hospital in May.