Why "nor do/shall I" is incorrect in this sentence?

I have previously asked this question here.

https://www.italki.com/question/391276

https://forum.wordreference.com/threads/nor-neither-do-shall-i.3306253/#post-16744673

But I still have some doubts.

If you don't go to the party tomorrow, ___________.
A. nor do I
B. nor shall I
C. neither do I
D. neither shall I

The key is D(but I believe C also has its merits). But I have looked up the word "nor" in my dictionary and find this usage

BrE used after a negative statement to say that the negative statement is also true for someone or something else:

For example,
'I don't want to go.' 'Nor do I.'
"They couldn't understand it at the time, and nor could we."
So I think this usage can also be applied to this test paper question, which means A, B, C, D are all correct?

Thank you.