It's best to ask your school because every school will be able to accommodate situations differently. A group of girls applying for scholarships in my year needed an extra GCSE, so the school put on the Additional Maths AS as a substitute, and they worked on that instead of GCSE maths during their maths lessons. There might be a teacher willing to work with you after school or at lunch time to get an extra GCSE if you want to put the effort in, but it's unlikely you'd be able to do an extra one in school time because it would be impossible to schedule. If you're given free periods you could inquire about doing one then? If you're really committed, you could even work on teaching yourself a GCSE over the summer and ask your school if they could enter you for the exam.
Currently, I'm only doing six GCSEs and two BTECs ; this may appear fine but the career that I want to go into requires seven GCSEs.
What are you doing, and any ideas what you'd like to do as an extra? The army is very keen on their officers having a good technical background (if you go to the Welbeck Defence Sixth from you have to do Maths and Physics A level) so an extra Maths related GCSE might be an idea.