I have put roughly 0 thought into answering this question, or whether it even makes sense within Scott's framework:

Finite factored sets are presented in some sense as an alternative/refinement to Pearlian causal graphs. 
In Pearlian causal graphs we can make the distinction between conditioning P(X | Y=y ) and intervention P(X | do(Y=y) ). What is the equivalent of P(X | do(Y=y) ) in the context of finite factored sets, if there is any? If not, how do we make an analogous distinction in FFS, or achieve the analogous thing that do is meant to achieve?

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Scott's framework doesn't have do, because do requires you to get "off the causal shell", to talk about causally impossible worlds, while finitely factored sets restrict themselves to only causally possible worlds.

Yes, thank you for asking this question.

I might expand - what is the exact relation between factored sets and DAGS?