Halliday & Matthiessen (2014: 475-6):
With the additive and adversative, however, there may be no conjunctive expression; such clauses are therefore identical with non-finite elaborating clauses, except that in speech they are not marked by tone concord. Examples:
||| So she wandered on, || talking to herself as she went. ||| (‘and talked’)
||| Hardly knowing || what she did, || she picked up a little bit of stick || and held it out to the puppy. ||| (‘she hardly knew ... , but she picked up ... ’)
But where the sequence is β ^ α, such a nexus is likely to be neither elaborating nor extending but enhancing;
The sequence in the 'extending: adversative' example is β ^ α (1 + 2).