 If there are latent common causes, so that the true causal structure on \(\bV\) is represented by an ADMG, then it may not be possible to discover the true causal structure using only single-variable interventions.  (Although we can do this in the special case where the functions in the underlying structural equation model are all linear.) However, if we can intervene on multiple variables at the same time, then it is possible to discover the true causal graph.