While it could be handled with extra categories, such as (s/(vp/np))/(s/np) for what, this is exactly the sort of strong-arm tactic that inclusion of the standard B, T, and S rules is meant to avoid.
the standard CCG analysis for English auxiliary verbs is the type exemplified in (16) (Steedman, 2000, 68), interpreted as a unary operator over sentence meanings (Gamut, 1991;Kratzer, 1991): this type is empirically underdetermined, given a widely-noted set of generalizations suggesting that auxiliaries and raising verbs take no subject argument at all (Jacobson, 1990, a.o.).