I've just seen yet another reason to issue the reminder that, whatever a quantum superposition is, we shouldn't really be saying that the system is "in two states at once."
So if you want to affirm that every state formed by adding two other states is a coherent superposition, you must posit that every self-adjoint operator is observable. But this last assertion is known to be false (for, e.g., the electric charge observable.) So care is required.