On Sunday, the Lambourn handler, who trains in partnership with Chris Grassick, confirmed that the Qatar Prix de l'Arc de Triomphe at ParisLongchamp on October 2 will be the five-year-old's next target, with the Japan Cup and the Hong Kong Vase also under consideration.
"The Breeders' Cup is after the Arc, so basically the Arc is next on the agenda and once you've won that race, you have a free entry to the Japan Cup, same as the Breeders' Cup, same as Hong Kong," said Muir.
"We can't do them all. It is impossible to do everything."
Martin Dwyer, who has partnered Pyledriver in all but four of the entire's 18 career starts, is currently recuperating following surgery to repair a torn ACL and hinted that a trip to Keeneland could be on the cards after the Arc.
Muir said: "The three owners and me, and definitely Martin - even though he is not riding, he is a big part of this horse's journey - will decide where we go after the Arc. The Breeders' Cup is possible.
"We will have a meeting and discuss which way we go, but the Arc is next."
Pyledriver's 18/1 success, beating five rivals by upwards of two and three-quarter lengths in the mile-and-a-half midsummer Ascot highlight, was run in a time of just under two and a half minutes.
He was 18 lengths clear of Irish Derby winner Westover and 25 lengths in front of unlucky Oaks runner-up Emily Upjohn, who represented the Classic generation.
Muir, who has been training since 1991, feels the victory under jockey PJ McDonald may be decried in some quarters, because Pyledriver is not stabled in a bigger yard.
"He is grand, really good this morning," Muir reported. "He has come out of the race well, he is very happy. I was out with him about 5am this morning and he is fine.
"Others might have a hangover, but I don't drink. A few of the boys who came in this morning were nursing!"
He added: "The horse absolutely deserves it, but it doesn't make a jot of difference.
"If this horse would have been trained by Aidan (O'Brien) or by John Gosden, he would be a superstar.
"It is no good saying 'it is one for the small man', and then go and say 'this horse didn't perform or that horse didn't perform, because he didn't do that or he missed the break'.
"Before the race, they said, 'Westover was a fantastic winner of the Irish Derby and was an unlucky loser in the English Derby… Emily Upjohn is the best we've ever seen - she bolted up at Sandown and won at York and she was unlucky at Epsom, if she had not have stumbled she'd have won the Oaks… Mishriff got the jockey sacked because he should have won the Eclipse last time… the German horse won his Group Two really well and won last year's Arc… Broome won the Hardwicke last time out' - not any giving a mention to Pyledriver!
"Then, after the race, (they say) 'none of them have performed'.
"But you can't take anything away from him - it was a real fast time."
Though the going ahead of the Group One contest was officially described as good to firm, Muir felt the ground rode easier and was fulsome in his praise for clerk of the course Chris Stickels for producing a surface he described as "perfect".
Muir also countered those who felt last season's Arc winner, Germany's Torquator Tasso, who chased home Pyledriver, did not have his optimum conditions.
"I walked the course and fair play to Chris Stickels. That course was in magnificent condition," said Muir. "That was good ground. That was not good to firm (good in places), that was beautiful, beautiful ground. Perfect ground.
"But they all forget, four runs ago, when I was going to Hong Kong, they said, 'Pyledriver is much better on soft ground'.
"Now we have gone and won, we are longer in the betting for the Arc than the horse who finished second, because they say the German horse will appreciate soft ground! I think people just don't know what they are on about."