When an AFM supplement is needed.
And with regard to griffo's original post .... how would you know what modifications to an aircraft are or are not approved without the update/supplement in the AFM .....
The approval certificate for the modification - this may be the FAA or EASA STC certificate, or the design approval document issued by the design organisation (Part 21J in EASA-land) will state when an AFM supplement is needed and will specifically list the supplement number, revision staus and possibly date of approval.
Under EASA, some modifications classified as 'Minor' can still have an AFM supplement approved via the Form 36 route - typically this can apply to Traffic Advisory Systems, BRNav compliance etc. A similar route exists under FAA rules where a local FSDO can approve an AFM supplement as part of the Form 337 approval process.