Turbo Linn could be in line for the Juddmonte Coronation Cup on June 6 following a pleasing seasonal debut at Hamilton.
The five-year-old went down by a fast-diminishing head when attempting to give 9lb to the race-fit Eradicate.
"She's come out of the race brilliant," said trainer Alan Swinbank.
"We are just going to make our minds up where we are going now. It depends on the ground but the next stage could be the Coronation Cup.
"There's a Group One in Dusseldorf and there's the Hardwicke at Royal Ascot, but that might be a tougher race and the ground might be a bit quicker there.
"We haven't an awful lot of options because she's not EBF (European Breeders' Fund) registered. There are one or two of those races that are EBF so that limits me a little bit.
"It's just one step at a time. It would be nice to get to Epsom if we could and I'd like to think the ground would be OK for that."
Swinbank is also targeting Haydock's Lancashire Oaks, which Turbo Linn won last year when the race was transferred to Newmarket.
"She has no penalty in the Lancashire Oaks this time, so I think that's where we'll be going in the first week of July," added the North Yorkshire trainer.
"She's in good form and Neil (Callan) is over the moon with her."
Getaway, trained in France by Andre Fabre, is also on course for the Coronation Cup at Epsom.
Last season's Arc de Triomphe fourth made an impressive reappearance when winning the Group Two Jockey Club Stakes at Newmarket two weeks ago.
"He's well and he will probably go for the Coronation Cup at Epsom," confirmed Paul Harley, racing manager to owner Baron Georg von Ullmann.