He remarks on page 70 that "if descriptive complexity results similar to ours can be established for larger language-theoretic complexity classes (for the indexed languages, for instance) it may be possible to make the argument that GB can be restricted to principles that are definable in the corresponding theory without losing the ability to account for the full class of natural languages."
what has been done for the (strongly) context-free languages might be also possible for larger classes, like the TAG languages or the indexed languages (Rogers [1998] shows that in fact this can be achieved for TAGs).