”いただけないでしょうか” has some meanings. いただく(changed いただけ) means, formal style of want to get (something) and eating. Another meaning is as formal asking, which use to need hoping to do something to someone(usually ask for an elder person and unfamilier person). 1.When you want to get something →Would( or Could) you give me (something)? 2.When you want to eat→ Would( or Could) you eat (something)? 3.Formal ask→ Would( or Could) you 〜？

Don't you want to eat?