In the English Vocabulary Profile at B1,
so did we/so have I/so is mine, etc. = someone else also does something or that the same thing is true about someone or something else
For example:
A: I‘m glad you‘re back.
B: So am I, dear boy.
“So am I” in the context above means: “I’m glad I’m back too.”
A search in iWeb for:
so BE _P .
1 SO BE IT . 10934
2 SO ARE WE . 1090
3 SO ARE YOU . 867
4 SO IS HE . 284
5 SO ARE THEY . 183
6 SO WERE WE . 159
7 SO IS SHE . 148
8 SO WAS HE . 148
9 SO WAS SHE . 80
10 SO IS MINE . 78
11 SO IS YOURS . 54
12 SO WERE THEY . 50
13 SO WERE YOU . 41
14 SO BE YOURSELF . 31
15 SO IS OURS . 18
16 SO WAS MINE . 17
17 SO IS THEIRS . 13
18 SO ARE YOURS . 13
so DO _P .
1 SO DO WE . 1358
2 SO DO YOU . 954
3 SO DID WE . 305
They all knew this could happen, and so did we.
4 SO DID HE . 262
5 SO DO IT . 245
6 SO DO THEY . 236
7 SO DOES HE . 189
8 SO DID SHE . 173
9 SO DOES SHE . 140
10 SO DID THEY . 135
11 SO DID YOU . 82
12 SO DOES YOURS . 29
13 SO DO YE . 26
14 SO DOES EVERYONE . 19
15 SO DO I . 11
16 SO DID OURS . 11
so HAVE _P .
1 SO HAVE WE . 201
2 SO HAVE YOU . 131
3 SO HAS HE . 45
4 SO HAS SHE . 28
5 SO HAVE THEY . 24
6 SO HAD SHE . 12
7 SO HAD HE . 11