Can vagueness cut out at any order?

Could a sentence be, say, 3rd order vague, but 4th order precise? In Williamson 19993. Williamson, T. 1999. On the Structure of Higher-Order Vagueness. Mind, 108: 127–43. [CrossRef], [Web of Science ®] View all references we find an argument that seems to show that this is impossible: every sentence is either 1st order precise, 2nd order precise, or infinitely vague. The argument for this claim is unpersuasive, however, and this paper explains why.