Number of definable degrees among simple exact nonnuclear algebras

Determine whether there are infinitely many or uncountably many definable degrees among simple exact nonnuclear C*-algebras.

Background

The paper identifies at least two relevant degrees: the common non-type-I nuclear degree and the strictly larger degree represented by the constructed simple exact nonnuclear crossed product. It does not determine how many further degrees occur within the simple exact nonnuclear class.

This question asks whether that class has an infinite or even uncountable hierarchy of definable spectrum degrees.