Most of the rest of the Temple treasures were probably looted and burned by the Germanic tribes that sacked Rome repeatedly.
One thing to keep in mind: if the Vatican actually had any of these treasures, don't you think they would have displayed them sometime before it became politically incorrect to do so? Wouldn't their be Churches dedicated to relics from the Temple? Wouldn't the Pope parade the Menorah around to celebrate his belief that the Church is the "true" Israel? The fact that there's no record of any of this happening suggests that the Vatican ain't got squat.
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