Remember that the school needs to know how many spots they have before their admissions goes out! So they need to know who is leaving.
But it’s not like it’s a secret that your child is applying: the school had to release the transcripts and everything.
I would be honest and upfront and say “We’re not set on boarding school. We want to see the offers. We really like your school, though. Can you give us an extra week?” They’re not going to love it, because they need to know how many spots they have to offer to new students, but it can’t hurt to ask.