Auxiliary verbs - so / neither

We can use so / neither / nor with an auxiliary to show that people have something in common
(something is the same about them).
'I'm looking forward to the picnic.'
'So am I.'
The statement is grammatically positive, so we replay with So. 'I haven't seen Paul today.'
'Neither have I.
The statement is grammatically negative, so we replay with Neither or Nor. Tim wants to go and so does Janet.
Mandy's not going on the trip and neither is Sue.

When used for short replies, the auxiliaries after so, neither or nor are the same as those in statement.
'We're going home.' Present continuous. Auxiliary: be.
'So am I.' 'I was looking forward to the party.' Past continuous. Auxiliary: be (past).
'So was I.' 'Tina's finished.' Present perfect. Auxiliary: have.
'So have I.' 'I'd never seen her before.' Past perfect. Auxiliary: have (past).
'Neither had I.' 'I'll have an orange juice.' Modal auxiliary: will.
'So will I.' 'I'd like to go.' Modal auxiliary: would.
'So would I.' 'I can't swim.' Modal auxiliary can.
'Neither can I.'
Simple tenses - present simple and past simple - do not use auxiliaries in positive statements.'I live in London.' Present simple.
'So do I.'
We use the auxiliary do in the reply.I played football yesterday. Past simple
'So did I.'
We use the auxiliary did in the reply.

There is no difference in meaning.'I don't want to go.'
'Neither do I.'
'Nor do I.'

The first syllable in the word neither 'nei-' can be pronounced in two ways.nei- rhymes with eye. This is more common in British English.
nei-rhymes with see. This is more common in American English.

As we have seen, we can reply with so / neither / nor + auxiliary +I when we have something in common with someone.
'I like this cheesecake.'
'So do I.' If we want to make it clear that we are different, other short answers are used.
'I thought the film was quite boring.'
'Oh, I didn't. I really liked it.'
The second speaker gives a short answer with an auxiliary I didn't and a short explanation. 'I don't like this music.'
'Really? I do. I like heavy metal.'