When you wish to ask for permission, you can say :

– Can I … please ? (eg. Can I go to the party please ?)
– Do you mind if … ? (eg. Do you mind if I go swimming ?)
– Would it be possible to … please ? (eg. Would it be possible to turn the sound down please?)
– Can I have permission to … please ? (eg. Can I have permission to use your bike please ?)
– May I … please ? (eg. May I have a pizza please ?)