Not so easy to counter the point about pastoral support, which is probably why I didn't comment!
Equally, I don't think it would be easy for the authority to justify any statement about the level of pastoral care.
The average amount of time a tutor or head of year has for each child will obviously decrease whenever an extra child is admitted, but the difference is not going to be earth-shattering.
There seems to be a constant drive to improve academic performance every year, and this is measured by SATs and exam results.
It is surely impossible to find anything equivalent where overall pastoral care is concerned because there are so many intangibles.
I wouldn't for one moment want to suggest that assessing the standard of pastoral care can be reduced to the level of examining the number of disciplinary offences, but you could try putting the admission authority on the defensive by asking: "Is there any evidence that standards have fallen when numbers have been above PAN? - For example, has there been a noticeable increase in the number of suspensions?"
I suspect that they won't know the figures, but if it turns out that there have been 6 suspensions instead of 4, don't allow the presenting officer to talk airily about a 50% increase unchallenged! If we are comparing year groups of 186 and 180, for example, one could just as well argue that the difference is between 6 out of 185 (3.22%) and 4 out of 180 (2.22%). That doesn't sound as compelling! Besides, one shouldn't draw conclusions from a single occurrence, so I would want to know whether this pattern is repeated every time there's been an oversubscribed year group.
Teachers tell me that, from time to time, they come across a "difficult year", and this seems to happen without rhyme or reason. I suspect it has little or nothing to do with "overcrowding".
It is so difficult to measure "pastoral care" in the fullest sense of the term that I doubt whether an assertion that it will suffer if numbers go above PAN can be proved one way or another.