Martin (1992: 220-1):
Simple additive relations realised through in addition, as well, additionally, besides which are used to extend a text can be opposed to cumulative ones like further, furthermore and moreover which build it up to something. Cumulative conjunctions are typically found in the context of an argument, conjoining messages causally supporting a thesis. Furthermore seems more common when more than two such arguments are being conjoined, moreover being the unmarked form when only two arguments are used.
 This is a false dichotomy: cumulating is 'adding to'. In SFL theory, this conjunctive relation between messages is construed as (positive) additive extension (Halliday & Matthiessen 2004: 542).
 All linguistic choices extend a text, not just conjunctive relations, and not just simple additive ones. This is 'extend' in the sense of 'increase the extent of', not in the sense of a logical relation.
 Despite contrasting 'extend' with 'cumulative', the cumulative conjunctions further and furthermore are listed in the system network (Figure 4.15) as realising extending, which is construed as a feature of cumulative. That is, a false dichotomy is reconstrued as a relation of hyponymy.
 The conjunction moreover is listed in the system network (Figure 4.15) as realising the other feature of cumulative, amplifying, though no argument is presented to justify the term in contrast to that of the other feature extending.