Never believed in getting vaccines at the same time. I know they say it is fine but really, it seems like a lot to trick your body into thinking it has two infections at once - plus the adjuvants are serious business. I don't know if I've ever actually seen a study on the efficacy of just one at a time vs two. At any rate, I spaced them for myself and definitely spaced vaccines for my kids when they were little. The Pediatrician gave me a tough time, apparently the argument for doing multiple is because you are in the chair and they don't want to lose the patient from a public health perspective which is risk when a patient walks away, but there was nothing that said it was better to do more than one vax at once for the individual.
I am getting ready for the new Covid one which I like before Halloween and if I do Flu it will be in November to cover from Thanksgiving and then reach as far into early spring as I can manage, Flu generally slams from Thanksgiving through April. Been doing this for ages and the timing seems reasonable.