The main benefit of scoring a Domestic Sleepers is this: your opponent goes, "WTF?" They will wonder why you'd include the card and perhaps adjust their play style because of it.

It goes well with fast-advance decks, where you have to score 3/2s, and it makes it so you really only have to score 3 agendas and a Domestic Sleepers in order to win. The same with 5/3 decks; they have to score 3 agendas and you only two. But, if they see you have six points and a DS scored, they're going to go all aggro on R&D/HQ next turn, so look out.

As said before, it's good for cards that make you forfeit agendas, like Archer and Corporate Town.

But that's about it for DS. Confusing them, having that seventh point, and forfeiting it. Not worth scoring more than one. Hard to include, but fun when you can.

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I've also found it handy as bait for Midseason Replacements. You get the tag storm without offering up any Agenda points to the runner. —
People play Midseason's as HB? —
The Board also turns this into a Ski.Kyu, but unfortunately is out of faction and costs a boatload of influence. —