A classification scheme is a small set of labels — public, internal, confidential, restricted is the common four — each attached to concrete handling rules: who may access it, whether it may leave the country, whether it may be used to train a model, how long it is kept, how it must be destroyed. The label is only worth having because of the rules behind it; a label with no consequence is decoration.
In practice. Four levels is the practical maximum. Every level beyond that produces edge-case arguments and inconsistent tagging, and the difference between "confidential" and "highly confidential" is almost never operationalized differently anyway.
Where it goes wrong. Classification is applied by asking data owners to tag everything, which yields the whole estate marked confidential — the safe answer for the person tagging, and useless for everyone else. Anchor the scheme in examples, default to internal, and require a justification for the top level.