This sounds like a question of how you're choosing to define a causal node. Is it something that's a fixed function of its parents? In which case your hypotheses about the function from A to B are hypotheses over different causal graphs. Or should the function from parents to node be a parameter that you represent inside a causal graph? In which case you need some representation of this distribution.

Either way, I agree that you need more than what you started with to capture the counterfactuals you're thinking of here.