Maybe ask him to read snippets of classic literature in English? broaden his perspective on the language. and you could ask him to read from his favorite korean literature in english. So he can practice working with and around the language barrier? reading from english books/works or translations of korrean books/works could also aid in growing his vocabulary.
Oh these are nice suggestions uou I'm actually going through SAT vocab lists with him, giving him a new word or two a day.
But in the end, my job isn't really to help him expand his English as much as speak it as fluently as possible. And out of all my students, he's probably the strongest in almost every area. It's mostly like, "what can I tell you to improve in the way you speak English", more than strengthening their comprehensive english (that stands like a secondary role, and isn't necessarily something I can write as an error).
I was mostly venting out of a feeling that I had to wrack my head to stretch for something for him to improve on, if only for the paperwork. it was like english class all over again ///flashbacks