I think 具体的(ぐたいてき）には is a translation for "to be specific". Also, the following phrase is often used: （もっと）具体的に言（う）と＝If I say (more) specifically, （もっと）詳（くわ）しく言（い）うと＝If I say in (more) detail, Furthermore, there is another phrase to fit your example. さらにいうと＝furthermore

We also say "もっというと" in the really casual way.