by extension

SO/CONSEQUENTLYused when you want to mention something that is naturally related to something else 自然地，当然地〔用于提及另一自然相关的事物〕

My primary responsibility is to the pupils, and by extension to the teachers and parents.

我主要是对学生负责，当然也对教师和家长负责。

Examples from the Corpus

by extension• Women lawyers, and by extension all professional women, looked for ways to balance family and work.

→ by extension at extension(1)