ちょうだい is noun, therefore by putting します（する） after the noun, you can make it formal speech. Actually, 頂戴 is not arrogant speech, littel kids are supposed to have used it arrogantly or abusively but 頂戴 itself not a bad expression to use. Rather, it indicates the close relationship with the person whom you are talking to when it is in good atmosphere. ちょうだい is allowed among your family members, close friends, a small restaurant which you used to go ,or your partner etc. But if you use this to youngers than you or the person whom you don't know or to the waitress in a big restaurant, it will be a bit oppressive sometimes. If the first person is always subject when using 頂戴. On the contrary, the second or third person is always subject when using 下さい to take something from other. ex) - Please give me water. 　（あなたは）わたしに水を下さい。 -I will take water from you. 　（わたしは、あなたから）水を頂戴（します）。 - 名刺（めいし）を下さい。　This is not polite expression when exchanging the name card at the business field. - 名刺を頂戴（いたします is more better）します。　Not bad, it would be appropriate when exchaiging the name card.