Trainer Mick Kent has the Group One Goodwood in his sights for Supido but the emerging sprinter is not yet guaranteed a start.
Supido made it five straight wins when he claimed a 1200m-Benchmark 84 at Flemington on Monday, his first start since February.
Kent revealed he was keen to run Supido in the Group One Newmarket Handicap at Flemington in March but the entire had a high white cell count leading up to the race.
He is now eyeing the Group One Goodwood (1200m) at Morphettville on May 21 but Supido may have to run again to get into Adelaide's feature sprint.
"I think we all know he's very smart," Kent said.
"I was actually going to run him in the Newmarket and on the Monday before he got a bit crook.
"I was hoping to run him last Saturday week but still wasn't quite right and then I wanted to run him in the Bel Esprit Stakes on Saturday but he got balloted out.
"So he ended up in a Benchmark 84."
A Listed victory in the Bel Esprit Stakes, won by Sheidel, would have made it easier for Supido to get into the better races.
"We're trying to get him into a nice race," Kent said.
"I'm going to nominate for The Goodwood and that's my aim. I'll look at the weights and if I have to run him again, I'll have to.
"Ideally I'd like to go straight in but I'll have to weigh up whether he's going to get a run or not. There seems to be quite a few horses heading that way."