The only times I see drillings or others with more barrels, it's on guns made for the European style of hunting, where pretty much anything that goes by the stand might get taken.
IIRC the term for guns with even more barrels is "vierling". There was a decent article in one of the old "Guns" annuals that showed a pile of the variants, with up to 7 barrels of assorted calibers all cobbled together.
You don't find a pile of them on this side of the waters.
Looks like a well made piece.
Does it shoot worth keeping?
Cheers
Trev