She likes jazz, and so do I.

Literal

She [topic-は] jazz [subject-が] like [is-だ] [but-が] I [also-も] [is-だ].

A compact 'me too' construction. 私もだ stands in for 私もそうだ, with the predicate そう ('that, like that') elided — the bare だ is enough since the context supplies the predicate. The clause-final が functions as a soft contrastive 'and yet' or 'but' connector — but in 'me too' contexts like this it reads more like English 'and.' Together, the construction is brisk and conversational, the kind of compact reply you'd give in casual chat.