Stacks should be first-class
If we make stacks fully first-class in S₀, then we can side-step the open questions about whether there should be a stack of stacks, or multiple discrete named stacks (à la Dawn), or any other higher-order arrangement of stacks. Instead, Swanson code could operate on stacks directly, however is most useful.
If stacks are first-class, is there some other existing language construct that we can model them as? I don't think we can model them as quotations, like you do in a non-linear stack language.