I wonder if there is a subtle difference between "1" and "2".
1. Will you go with me?
2. Will you come with me?
Not a teacher.
'come with' might stress the idea of accompanying me somewhere
'go with' might stress the idea of going somewhere (with me)
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I'm not a teacher
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In general, you should use come for movement towards the place where the speaker is or will be e.g.
Come and see me at my office.
I could see them coming down the hill (=getting nearer to me).
When are you coming home (=to our home)?
and go for movement in other directions e.g.
Are you going to Sally's tonight?
I wish he would go home (=to his home, away from me).
Longman
I've also found the same question on BBC - Learning English. And here's the answer:
Note, however, that come with and not go with is normally used when we are talking about joining a movement of the speaker or hearer, even though the movement is away from their current place or position:
I'm going to the hospital this afternoon to get the test results. Could you come with me?
We're going to Egypt for a week at Christmas . Would you like to come with us?
http://www.usingenglish.com/forum/as...e-go-back.html
BTW 'go with' might also imply starting some sort of relationship.
You asked a similar question on 3 February, and I referred you to this:come or go back