The rules are set out in the Admissions Code.
Academies are required by their funding agreements to comply with the Admissions Code and the law relating to admissions, though the Secretary of State has the power to vary this requirement where there is demonstrable need.
There's a link to the Admissions Code in our Q&As (A4).
If you're thinking of variations to the PAN - as opposed to determining the PAN - then the Code states:
3.6 Variations - Once admission arrangements have been determined for a particular academic year, they cannot be revised by the admission authority unless such revision is necessary to give effect to a mandatory requirement of this Code, admissions law, a determination of the Adjudicator or any misprint in the admission arrangements. Admission authorities may propose other variations where they consider such changes to be necessary in view of a major change in circumstances . Such proposals must be referred to the Schools Adjudicator for approval, and the appropriate bodies notified. Where the local authority is the admission authority for a community or voluntary controlled school, it must consult the governing body of the school before making any reference. A variation to increase a school’s PAN is not required to be referred to the Schools Adjudicator. [footnote 56: Section 88E of the SSFA 1998. Academies do not have to refer proposed variations to their admission arrangements to the Schools Adjudicator, but instead seek agreement with the Secretary of State.]