可不可以 is the A-not-A question form of 可以 (can/may). It is used to ask for permission or to inquire about possibility, equivalent to 'Can (I/you/we) or not?' or 'May I?'. The structure is fixed: 可以 + 不 + 可以, and it always appears as a single question phrase, typically at the beginning of a sentence or before the main verb.