Aux NP -- as in so do I, so are you, so has Mr. Smith -- is a formulaic tag construction
that indicates a deletion, and must be preceded by a clause containing the deleted material.
- You believe that he lost the race, and so do I.
- She's an idiot, and so are you.
- I've been there frequently, and so has Mr. Smith.
In the first sentence, so replaces 'believe that he lost the race';
in the second, it replaces 'an idiot';
and in the third it replaces 'been there frequently'.
The order of the
Aux and the so is reversed in this construction, the way it is in a tag question.
Normally so would follow the
Aux, as it does in
- I've always wanted to fill out my own tax forms, but I've never done so.
Here so replaces 'fill out my own tax forms'
All of these constituents that so replaces are Verb Phrases (VPs).
If a pronoun like it can replace a noun,
and a pro-verb like do can replace a verb,
then the proper term for so is a pro-VP.