Dudley is a Mutant/Olympian Half blood (roman or greek)/becomes a member of the Western Soul Society after dementor attack/is a Meta human (DC-verse)/is actually targeted by a terminator sent by skynet because he is key to Defeating it in the future.

Basically any kind of crossover, at any point in the books, where the Dursleys have to face the fact their son is just as non-normal as Harry, if not moreso.

Perhaps it comes out while Harry is at hogwarts and they try to keep it from Harry. Perhaps Dudley's always been able to do things and has just been blaming Harry (bonus if Dudley gets discovered/caught after they left Harry at King's Cross because Dudley's become so used to using his ability and blaming Harry that he uses it/blames Harry when he forgets Harry isn't there to be blamed).