I didn't realise schools still had specialisms like STEM tbh. But if the appeal school does, and your DC has a demonstrable interest, then that would be worth a mention. You would need evidence of interest tho - I am thinking attendance at holiday science clubs or events or science days at local museums, that kind of thing.
If you were refused a school place, that is because the school is full. You then need to show that the detriment to your child of not attending that school is greater than the detriment to the school of going over PAN.
As above, useful things might be clubs, subjects or other offers from the appeal school that you can evidence interest in.
For example - a child who has done lots of drama and music in primary and can show evidence of ability and interest, and a school which has a strong offering in drama and music, offers music GCSE, offers drama GCSE, while allocated school does not.
Factors like transport, friends going there, convenience for you, good Ofsted, good results unfortunately are not taken into account.