There's been suggestions for years about how the US federal government should break up companies that are "too big to fail", i.e. their failure would pose a systematic risk to the entire economy. The federal government is clearly unwilling to actually consider this. But could a state government forbid such a company from operating in their borders? Could Tennessee, to pick my own, declare that all Citibank operations must cease in the state?
It is unconstitutional to make a law which is explicitly against a specific entity ("Citibank must not operate in our state") but they could make a more general law which applies to all entities which fulfill certain criteria ("Banks with an international business volume of more than X and any of their subsidiaries must not operate in our state"). An actual law would of course need to be a lot more complex to close any of the bookkeeping loopholes big banks would find and exploit immediately, but you get the idea.
However, when the goal is to prevent another banking collapse, such a law would be counter-productive. It would hurt the big banks affected by it and could cause one to collapse, which would result in the feared banking collapse spiral.
It would also hurt the economy in the state as a whole, because it would not just drive the big banks out of the state but also all the companies which make business with them.