Would you please explain the usage of the expressions “So do I” (its variants such as ‘nor can I’) and “Me too”?
When can we replace “So do I” and its variants with “Me too”?
And, how do we call such expressions?
(1) "Ed will certainly notice the mistake and so will Max ___ ".
(2) "Kim can't see any advantages of being in the EU, and nor can I ___".
(3) "Jill likes going on holiday to Turkey, and Jane ____ too".
In (1) and (2) "so" and "nor" combine with subject-auxiliary inversion in a special kind of 'ellipsis'. In both examples, there is a very clear anaphoric relation between the second clause and the first: we understand "Max will certainly notice the mistake", and "I can't see any advantages of being in the EU". "So" and "nor" are best seen as connective adverbs here indicating likeness between the two clauses. The gap marked by ___ indicates where the ellipted predicate would go in a tree diagram.
Things are slightly different in (3). Here "too" is also a connective adverb, but there is no inversion. The ellipted constituent marked with ___ is "likes going on holiday to Turkey", so we understand that "Jane likes going on holiday".
You gave the example "so do I". It's the same as the other examples:
"Ed wants to go to Spain for our holiday, and so do I ___".
This is just like the examples I gave you with "so will Max" and "nor can I", where "so" is seen as a connective adverb. In this example, the ellipted predicate (marked by gap ___ ) is "want to go to Spain for our holiday".