Doran (2021):
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[1] To be clear, Halliday & Matthiessen (2014: 451) explain a multivariate structure as follows:
A multivariate structure is a configuration of different functional relationships, like Theme + Rheme, Mood + Residue + Moodtag, or Actor + Process + Recipient + Goal. Note that, although it is the functions that are labelled, the structure actually consists of the relationships among them. While we have modelled all multivariate structures in terms of constituency, this structural mode is in fact most appropriate for the experiential mode of meaning. That is, the relationships among the elements in a multivariate structure can be characterised as segmental from an experiential point of view but as prosodic from an interpersonal point of view and as culminative from a textual one. A prototypical example of a segmental structure is the transitivity structure of a clause, a prototypical example of a prosodic structure is the tone contour that typically extends over a clause, and a prototypical example of a culminative structure is thematic prominence at the beginning of the clause (followed by rhematic non-prominence).
That is, in SFL Theory, the number of occurrences of a functional relation is irrelevant. For example, the experiential structure of a clause can feature multiple circumstances, and the interpersonal structure of a clause can feature multiple Adjuncts.
[2] To be clear, Halliday & Matthiessen (ibid.) explain a univariate structure as follows:
A univariate structure is an iteration of the same functional relationship: for example ‘and’ as in Bill Brewer, Jan Stewer, Peter Gurney, Peter Davy, Dan’l Whiddon, Harry Hawk, Old Uncle Tom Cobbley and all; ‘equals’ as in Tom, Tom, the piper’s son (Tom = Tom = the piper’s son); ‘is a subset of’ as in newfashioned three-cornered cambric country-cut handkerchief (what kind of handkerchief? – country-cut; what kind of country-cut handkerchief? – cambric, ... ); and so on. Such iterative structures are unique to the logical mode of meaning; they are, as noted, formed out of logico-semantic relations.
Importantly, iteration is the underlying principle of all univariate structures, because the second and subsequent units of a logical structure are each singly generated by re-entering the same network that generated the first unit. Matthiessen & Kasper(1987: 46):
Logical systems are assumed to be (linearly) recursive. The recursion is represented by a loop back to the entry condition in the system…