One aspect of P4C which often gets missed is to identify the key concept in a question and then stretch it or explore it more to deepen understanding. If this is done, the dialogue in an enquiry can go much deeper. It can be done before an enquiry or even in the middle of enquiry.
P4C can also be a great way of engaging with a school's core values. For example, if one of your values is compassion it is worth taking time to think, What could compassion look like in our lives? In our school? Staff or students could generate and discuss their own examples, or they could sort these into which of these 10 examples are definitely compassion, which are not and which are borderline:
helping a friend
standing up to a bully
doing someone’s homework for them
putting your arm around someone who is crying
giving money to someone begging on the street
giving to charity
giving someone a hug
giving a present
being polite
going without food so someone else can eat