Notice that while the predicate (e.g., shall (I/we) eat . . . ) is used only once in English, the predicate is repeated in Korean.
Meanwhile, when -(으)ㄹ까요? is used with other verbs such as 하다 “do” and 생각하다 “think,” it expresses the speaker’s provisional idea regarding what s/he may do, corresponding to “I am thinking of doing something” in English. Consider the following sentences: