its rare to see a gun with more than two barrel sets, problem is you don't need more guns than.
on egun ist just know a Meffert 16 ga double with 16 ga +11,16x60R combination gun barrels and new made 16 ga + 5,6x52R combination gun barrels by Wolf/Suhl

https://www.egun.de/market/item.php?id=19318664#img