How should I use "so" and" too" for implying "That's also true for me" in this example?

The second conversation does not flout any of grammatical rules of eliding and is correct in its formal/ informal avatars.

The first conversation is our problem area. It is proposed that B wants to skid most of the words by restricting the answer to bare minimum. We call it Answer Ellipses. Ellipses come from Greek meaning 'to leave'. In our day to day conversation words are left out of a sentence, but the sentence can still be meaningful and in such an elliptical construction of answer, redundancies are left out when context is of real help.

But we must be careful the Answer Ellipsis can satisfy the identity requirement( parallelism) needed to license deletion for likeness of form enable the reader/ person spoken to recognize the likeness of content and function. @Lawrence suggested the best possible grammatically correct alternatives.

• Mine, too.
• So of mine.

• Mine, also. or any other form as:-

• Yes, I do, incidently my teacher too.

In answer ellipses or dialogues we can skid the whole of sentence except a word or two. Symmetry only matters.