を差し上げましょう

shall I give you

→ を
phrase Rare #45,467
shall I give you 差し上げる is a humble, polite way to say “give” when giving something to someone.
JA: こちらの資料を差し上げましょうか。
EN: Shall I give you these materials?

飲み物を差し上げましょうか。

Would you like something to drink?