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Can you explain to me the reasoning that "You could get me and John a book".

I did find this: Many people mix up the personal pronouns I and me. To avoid trouble, delete the other person from the equation and see what you’re left with. If you’ve written Sandra and me find that offensive, take away Sandra. You’re left with Me find that offensive. That sounds strange, so you know that I, not me, is correct. (refer to http://www.sparknotes.com/writing/style/topic_111.html )

However the sentence of "You could get me a book" sound so wrong.

Help!
Comments  
My try:

"Get a book" sounds incorrect to me. I would say "bring us a book" in short so that I will not have to think about the correct usage of "me and I". Emotion: stick out tongue

Ehem, "me and I" are in object case in the sentence and (because of this) "me" is correct.

Bring it to me.

Bring it to Jonh. Bring a book to John and me.
I don't see what sounds so wrong about it. If you turned the sentence around and said "Could you get me a book" it might sound a bit better though.
Students: Are you brave enough to let our tutors analyse your pronunciation?
A: Ugh. I just don't know what to get you for your birthday. You never hung up the self portrait I make you from the string and stuff I collected from the streets, and you didn't like my home-brewed mouthwash either. I know, you pretended to like it, but you poured it down the drain as soon as I left. And my homemade cornflake-covered pineapple lasagna wasn't a hit with you either. I just don't know what to get you.

B: Erm, uh... you could get me a book. I like books.
Thank you GG! I really didn't know this structure. It really helped me.

To Anonymous:

No need to be angry gal, we are all here to learn.

Are you referring to the 2nd reply? If yes that was mine and it certainly wasn't supposed to have an angry undertone.

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It does not sound strange at all because it is correct. Who else would you gte a book for? I? Also, the sentence "sounds" not "sound" as the sentences "sound" is correct?