Halliburton supported the president’s campaign, as did all the other big companies of corporate America.
"I love Icelandic films." "Really? So do I."
"George can eat fifty eggs in an hour!" "So can my brother!"
"I am not going to Andy’s party tonight." "Nor/Neither is Susan."
"My family have never been on a holiday abroad." "Nor have mine."

Note that if we express an opposing view, there is no inversionA structure in which a verb or an auxiliary precedes the subject. E.g.: "Here comes the sun.":

"I love Icelandic films." "Really? I don’t."

Partial inversion in questions
Partial inversion Revision questions: inversion