For most states, there's only two governments--the city and county governments of most states are organs of the state governments and only have such authority as the state unilaterally deigns to let them have.
As for the distinction between state and federal, that's essentially the exception that proves the rule. The reason you cannot have multiple governments is because you end up with a situation of contested authority, and a brief look at US history (and I suspect every other federal system in the world, though I don't have particular knowledge for others) shows a litany of debates over whether state or federal government has primacy in a given jurisdiction. It's only barely tolerable by the fact that, even if the grant of authority to the different governments is unclear, at least the authority to decide who has authority is unquestioned.
As for the distinction between state and federal, that's essentially the exception that proves the rule. The reason you cannot have multiple governments is because you end up with a situation of contested authority, and a brief look at US history (and I suspect every other federal system in the world, though I don't have particular knowledge for others) shows a litany of debates over whether state or federal government has primacy in a given jurisdiction. It's only barely tolerable by the fact that, even if the grant of authority to the different governments is unclear, at least the authority to decide who has authority is unquestioned.