"As three men have now been charged, aspects of the investigation including the injuries Benton suffered will not be released."
One man has already appeared in court on charges related to the alleged gang-related attack.
Terence Junior Whaanga, 25, of no fixed abode, appeared from custody briefly at Christchurch District Court this morning charged with injuring with intent to cause grievous bodily harm.
He made no application for bail and Judge Raoul Neave remanded him without plea in custody until April 9 for an appearance via audio visual link.
Parata's death has sparked several violent incidents in prison that has raised safety concerns by the Corrections Association.
In the latest alleged incident on Tuesday, a prisoner was attacked at about 2.30pm.
He was taken to Christchurch Hospital but returned to Christchurch Men's Prison later that night.
Christchurch Men's prison manager John Roper confirmed Tuesday's assault.
"Staff immediately intervened and contained the incident and the prisoner was taken to hospital for assessment and treatment," he said.
Parata's suspected murder is just the eighth such case in the past two decades.
But gangs expert Dr Jarrod Gilbert, a spokesman for penal reform group Howard League, fears that gang revenge could "snowball" out of control.
The atmosphere inside some areas of the prison would now be "very tense", Dr Gilbert said.
"Staff will need to be extremely alert in coming days and longer to ensure that the violence does not spread and snowball," he said.
"As a general rule, longer term prisons want to just get on with their lags, but things like this breed retaliation -- in fact, often they demand it."
Long lockdowns and careful segregations will be used to quell the violence, said the author of Patched: The History of Gangs in New Zealand.
"One can only hope, perhaps, that grieving does not lead to more tragedy. And that justice is served by the courts and not in the prisons. But again, prisons often run on their own rules," Dr Gilbert said.