How to handle falling down stairs?

It is well-established in fiction — as in real life — that falling down a flight of stairs is dangerous. A significant tumble can seriously injure or kill a person. "Pushed down a flight of stairs" is by now a hackneyed modus operandi in crime dramas. Recognizing that D&D is not a physics simulation, how should a DM model that danger?

Under normal falling rules, "[a] fall from a great height" deals 1d6 damage per 10 feet fallen. (PHB p. 183.) That wording seems to presume a freefall ending in a single, hard impact. Falling down stairs is at least arguably different: it doesn’t involve the same velocity, but it might involve a lot more bludgeoning.

Do the normal falling rules cover falling down stairs? Are there any alternative rules in published 5E materials? If it helps, our table does use the optional falling rules from Xanathar’s Guide to Everything, although so far we haven’t treated those rules as answering this question.