Is an interrogative sentence like “So did you?” or “So is she?”, possible?

A: Mike came here yesterday.
B: Possible responses: (1) Did you, too? (2) So did you?

Instead of saying, “Did you come here yesterday, too?”, can you say, (1) “Did you, too?” and (2) “So did you?”?

Are (1) and (2) both OK?
If (2) is not OK, could you tell me why?

How about this situation?: Jane has two daughters, Grace and Emily.
When Jane shows you a photo of Grace and you, knowing that she has two daughters, say, (3)”Grace is beautiful.”, can you add to it, “So is she (Emily)?”, meaning, (4)”Is Emily beautiful, too?”

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