Secret filming by the BBC programme broadcast last month showed residents being pinned down, slapped and taunted at Winterbourne View, near Bristol.
Police investigating the matter confirmed a further two men, aged 26 and 32, had been arrested and bailed.
Local MP Jack Lopresti has called for the hospital to be closed.
Eleven people have now been questioned in connection with the inquiry.
Earlier this week police arrested two women, aged 22 and 21, and three men, aged 58, 40 and 28. Last week, a woman and three men were arrested.
All have been released on police bail.
On Wednesday, it was revealed that South Gloucestershire Council staff may have been been told five times in two months about fears of abuse at Winterbourne View.
An e-mail from the hospital manager last November said "five safeguarding concerns" appeared to have arisen.
It is thought this may refer to concerns raised with the council's Safeguarding Vulnerable Adults panel.
The e-mail, sent by the manager to support workers and nurses and seen by the BBC, said patients had complained of ill treatment.
It said they had allegedly been teased, forced to swallow medication, threatened, restrained when it was not warranted and called nicknames which other patients then used.
The private home, which is taxpayer-funded, is to be investigated by the Care Quality Commission.
Hospital owner Castlebeck has apologised and suspended 13 employees - including the manager who wrote the e-mail.
Jack Lopresti, the MP for Filton and Bradley Stoke, has now called for the care home to be closed and for an independent review into what led to the failures in patient care.
The Conservative MP said: "I will be meeting with the chief executive of Castlebeck shortly to suggest that the company permanently closes Winterbourne View at the earliest opportunity.
"I am also calling for an independent inquiry into why such serious failures occurred and what lessons can be learnt to ensure the abuse at Winterbourne View Hospital never happens again.
"I believe that a truly independent inquiry is needed to restore the public faith in the care system."
The vulnerable patients filmed by Panorama have been moved to safety.
Two more people have been arrested in connection with the alleged abuse of vulnerable adults filmed by Panorama at a residential hospital.