I'd like to give my dog some water. Could you please give me some?
Could you possibly give me some water for my dog?
この場合、次のように聞くと良いですよ。
ーI'd like to give my dog some water. Could you please give me some?
「犬に水をあげたいのですが、水をいただけますか？」
to give my dog some water で「犬に水をあげる」
ーCould you possibly give me some water for my dog?
「犬のために水をいただけないでしょうか？」
Could you possibly ....? で「…していただけませんか？」
ご参考まで！
カナダ 
