The first horse to show symptoms has so far returned two negative and two positive results. Further testing is being undertaken.
Agriculture officials now advise that two further horses in the state's north-west are under investigation.
"An experienced horse vet has examined the horses and reported mild symptoms that are consistent with equine influenza," a spokesman for the Department of Primary Industries said.
"Blood samples and nasal swabs have been taken for testing at [the department's] Mt Pleasant laboratories and the Animal Health Laboratories in Geelong."
The new suspect cases were picked up in tracing and surveillance by the department's disease control centre.
The extension of the horse standstill means that all horse events scheduled for at least the next few days, including thoroughbred and harness racing, are off.