The defendant attended today's hearing by video link from the prison and remained silent throughout.
Name suppression was continued by Justice Robert Osborne at the request of counsel John Westgate.
At a previous hearing, the court heard, a psychological report had been sought by the defence and now an independent assessment was in process.
Suppression will be argued at a hearing in August.
Justice Osborne remanded the defendant to appear in court again on August 3.
Victims Vanessa Andrews and her partner Jorge Fuenzalida - Corrections officer - released a statement last week saying the incident was still very much on their minds.
"We try to help people where we can, and that day we heard people in distress. During the process we both got badly injured," they said.
"We still have a long way to recover, but we are getting there one day at a time with some good days and some not so good days."
Countdown senior manager Dallas Wilson, who spent a week in hospital, said he was stabbed four times and was lucky that no vital organs were hit.
The father-of-two paid tribute to those at the scene who assisted, as well as police and medical staff.
Security staff have been stationed in the supermarket since the incident.
