It is well-known that the theory of separably closed fields of some fixed positive characteristic and degree of imperfection is stable but not superstable. By a result of Cherlin and Shelah a superstable field is algebraically closed and many $\omega$-stable expansions of algebcaically fields are known ("coloured fields").

Is there an example of a non-$\omega$-stable superstable theory of (an expansion of) a field?