Connections of Toscanini have yet to map out a plan for the Anglesey Stakes runner-up following his fine run at the Curragh.
The son of Shamardal finished second for the third consecutive time in Saturday's Group Three contest and he has shown some excellent form in four career outings.
Sporting the royal blue silks of Godolphin, he finished third to subsequent Coventry Stakes second Cappella Sansevero on his Naas debut in May, before running a head second to Kool Kompany there in Listed company and again grabbing the silver medal in the Chesham Stakes at Royal Ascot last month.
Trainer Mick Halford said: "I'm happy with how he's come out of the race on Saturday and he was in good form this morning.
"He's yet to win a race but still boasts a rating of 104 and that just shows you how well he's done up to now.
"There is no definite plan with him. I'll sit down with the owners to discuss where we'll go next but I'm really pleased with how he ran again on Saturday and he's an exciting horse going forward."