Moderate Pragmatic Invariantism has been criticized in the literature for postulating implicatures that are not straightforwardly cancellable. Defenders of MPI have responded that the data are not as clear-cut as one might wish. This paper grants the defenders of MPI, for the sake of argument, that the implicatures in question are cancellable and then turns this admission against them. In particular, the paper offers Bank Case variants in which the conversational implicatures postulated by MPI are contextually suspended – and thus cancelled. Since our intuitions do not vary between the original Bank Case and these novel types of cases, the explanation offered by MPI must be mistaken. Our varying truth-value intuitions in the Bank Cases cannot be accounted for by means of conversational implicatures.