Yes, for you to win at stage 1, the panel would have to decide that the school had not made its case and
that it could cope with the admission of all
the appellants. [The only other possibility would be that a flaw in the admission arrangements comes to light at stage 1, and it is clear that one or more children should have been offered a place if the correct procedures had been followed - but this won't apply to late transfers where there were no vacancies to start with.]
It seems to me that, in reality, the degree of prejudice could vary from mild to extreme, so even if prejudice is established at stage 1, you may still succeed in denting the school case, and this can be taken into account at the balancing stage.
If your headteacher reads the latest Appeals Code, he'll find no mention of "fixing a number" at stage 1 of multiple appeals! I leave it to you whether or not to bring him up to date.