ご質問ありがとうございます。
「一緒に」はtogetherと言います。例:We played games together.(一緒にゲームした。)
「読み進めたい」はwant to read onとwant to continue readingと言えます。
例文:I want to continue reading this Daily News article together.
(先生に喋る時にはtogetherをwith youに入れ替えることもできます。)
ご参考いただければ幸いです。
I’d like to read through it together with you. Can we go through this article together?
I’d like to read through it together with you.
Can we go through this article together?
I want to keep reading along with you.
I’d like to work our way through this Daily News article together.
Could we read it together and talk about it as we go?
「読み進める」は go through / read through / work through が自然です。
日本語の「読み進める」は、
“最後まで読む”よりも「途中で止まらず、順番に一緒に確認していく」感じですよね。
* go through(順番に確認しながら見る)
Can we go through this article together?
は「この記事、一緒に順番に見ていけますか?」という、授業・レッスンっぽい自然さがあります。