The storming of AAMI Park during the clash between Melbourne Victory and Melbourne City left a player, referee and TV cameraman injured.
Images of eight men released on Sunday night showed one holding a bucket of sand, another holding a lit flare in the stands and another hanging from a goalpost.
Two men were identified after coming forward to police on Sunday, with another two following suit on Monday.
The latest pair identified include the man seen throwing a metal bucket full of sand used to dispose of flares.
No arrests have been made so far.
The bucket hit the head of City goalkeeper Tom Glover, who suffered a cut requiring stitches and leaving him with a suspected concussion.
Referee Alex King, who went to protect Glover, was also struck by the bucket.
Premier Daniel Andrews said the scenes from Saturday night were shameful and condemned the violence.
He warned the "cowardly" pitch invaders yet to hand themselves in to police, they would feel the full force of the law and soccer authorities.
"That's a venue that's owned by every single Victorian and I think the vast, vast majority of Victorians would have been sickened, as I was, to see that," Mr Andrews told reporters on Monday.
Asked about possible reputational damage from the ugly scenes ahead of Australia hosting the 2023 FIFA Women's World Cup, Mr Andrews said most Victorian major event crowds didn't behave that way.
"That's why it's so jarring. That's why it's such an affront," he said.
On Sunday, Victoria Police Acting Superintendent Jason Goddard branded the behaviour of the alleged pitch invaders as "disgraceful".
The chaotic scenes resulted in the game being abandoned in the 20th minute after Victory fans stormed the pitch.
A flare had earlier hit the Network 10 TV cameraman in the back of the head, which police said left him with a contusion and burned clothing.
The outbreak of violence made worldwide news and Victory issued a late-night apology to those affected.
Both sets of fans had planned to walk out at the 20-minute mark as part of a protest over the Australian Professional Leagues' decision to sell the next three grand finals to Sydney.
The crowd chanted "f*** the APL" while unfurling banners pre-game and during the match, and throwing flares onto the playing arena.
But the situation escalated when a flare from the Victory active area hit the cameraman and exploded, and Glover picked up another flare off the ground and threw it back into the stands.
Football Australia, which manages judiciary matters, has promised heavy penalties and "strong sanctions" against those found to be responsible, while also issuing a show cause notice to Victory.
The club has until 9am AEDT on Wednesday to show why it "should not face serious sanctions for bringing the game into disrepute through the conduct of its supporters".
