Can I get an extra pillow?

Literal

Spare-[appositive-の] pillow [object-を] please.

予備 ('spare, backup, reserve') + の links to a noun for an extra item; 予備の~をください is a useful one-liner for any hotel or airline request. Note how Japanese doesn't add politeness through indirection the way English 'Could I have...' does — ください is just the polite-casual baseline for asking for objects.