Can an air transport undertaking, especially one that has an AOC, operate (within EU land) occasional flights as PRIVATE. ????
Yes. It is even possible for an individual aircraft, registered on an AOC, to switch to making private flights, then switch back to PT flights on the next flight. Not easy to get authority, but it is possible.
Ironically, as others have hinted, it is probably more "illegal" to (potentially) charge for sandwiches on the flights...