However, Coordination facts seem to undermine this hasty conclusion: thus, consider the following:

(43) [Your sister could go to College], but [would she get a degree?]

The second (italicised) conjunct is a Clause containing an inverted Auxiliary, would. Given our earlier assumptions that inverted Auxiliaries are in C, and that C is a constituent of S-bar, it follows that the italicised Clause in (43) must be an S-bar. But our familiar constraint on Coordination tells us that only constituents belonging to the same Category can be conjoined. Since the second Clause in (43) is clearly an S-bar, then it follows that the first Clause must also be an S-bar — one in which the C(omplementiser) position has been left empty.