The art installation lavatory, valued at around £4.8m, was allegedly taken in the overnight raid at the 18th-century estate.
On Wednesday, the force announced that three further arrests had been made in connection with the burglary.
A force spokesman said: “A 35-year-old man, a 34-year-old man and a 36-year-old woman, all from Oxford, were arrested on suspicion of conspiring to commit a burglary other than a dwelling.
“They all remain in police custody.”
The fully-functioning toilet named America had been plumbed in for visitors to use in a wood-panelled room.
A man from Evesham was previously arrested on suspicion of burglary, along with a man from Cheltenham who was arrested on suspicion of conspiracy to burgle.
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