Halliday & Matthiessen (2014: 270-1):
These may be difficult to differentiate from circumstantial elements in the transitivity structure of the clause. To differentiate them in analysis, we can apply textual probes: in principle, being an element of the clause, a circumstance is subject to all the different textual statuses brought about by theme, theme predication and theme identification.
Thus with it in so you have to be beautiful with it is a circumstance (of Accompaniment), if we interpret the clause to mean ‘so you and it [silver] have to be beautiful together’, since it can be Theme (so with it you have to be beautiful rather than so it you have to be beautiful with) and predicated Theme (so it is with it that you have to be beautiful rather than so it is it that you have to be beautiful with).
In contrast, a Qualifier cannot on its own be given a textual status in the clause since it is a constituent of a nominal group, not of the clause; so it can only be thematic together with the rest of the nominal group that it is part of. …
However, there is a considerable degree of indeterminacy in this area …