IMO, your do does not fit in at all in the proposed format/order. Some might argue that with a shifted position of your proposed do , the do might place an accent on the desire to read again the book: Any really great book we do want to read the second time even more than we wanted to read it the first time. I'm not so sure.
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TakaYes.
would it sound strange to you native speakers?
DavkettI'd probably go with Marius on a rewrite, except I'd put a comma after 'book'.I agree with the comma, wasn't sure if others would feel the same about it.