Optimality Theory has been adapted by some linguists to a stratified model, what are the benefits of such a model over a non-stratified model of OT?
Stratal approaches offer a way to deal with morpho-phonological opacity, which is one of the biggest challenges to the traditional monostratal version of OT.
A few years ago I looked at some inflectional paradigm data from several languages--Japanese, Ukrainian, and Turkish. In each of these languages I found a handful of forms that on the surface appear to violate the expected inflectional pattern (e.g. in Japanese there are some verbs that consist of vowel-final stems and vowel-initial suffixes, despite the tendency everywhere else for vowel-final stems to "select" consonant-initial allomorphs of suffixes). I found that, in each case, no single ranking of constraints could account for the majority of forms plus these exceptional forms.
It turned out that adopting a stratal model--one with a unique "stem phonology" constraint ranking and one with a unique "word phonology" constraint ranking--could account for all of the data.