Halliday & Matthiessen (2014: 637-8):
With a declarative response, if there is a change of Subject only, we may have substitute so, nor, neither in initial position ( = ‘and so’, ‘and not’) followed by the Mood element.
... but I heard some water in it. – I did too. – So did I.
I love them. – So did I. – Me, too.
||| This drags down the bibliophiles’ score; || and so does the disgraced Nixon, || ranked at 23 in Siena. |||
I didn’t want to see it all. – No, neither did I.
The order is Finite ^ Subject (to get the Subject under unmarked focus). If the Subject is unchanged, so that the focus is on the Finite, the order is Subject ^ Finite:
S04: At their age you were an orphan. You didn’t have to. – S05: Not quite. – S04: You were. – S05: Oh yes. So I was.
The negative has various forms:
They’ve never replied. – So they haven’t/Nor they have/Neither they have [∅: replied].
Not infrequently, the Residue is substituted by the verbal substitute do, as in:
They say an apple a day keeps the doctor away. – It should do [∅: keep the doctor away], if you aim it straight.
If the focus is on the Residue (and hence falls on do), the substitute form do so may be used (as an alternative to ellipsis):
||| Tempting as it may be, || we shouldn’t embrace every popular issue [[ that comes along]]. ||| When we do so || we use precious limited resources || where other players with superior resources are already doing an adequate job. |||