Hospital bosses called in police on November 8 after concerns about the treatment of patients on the stroke unit.
A day after an nurse was arrested on suspicion of poisoning patients - or "administering any poison or noxious thing with the intent to injure and ill treatment or wilful neglect".
Last week, she was re-bailed until February next year.
All three medics have been suspended by the hospital, which said it flagged its concerns with police "immediately".
How many victims are there?
The Gazette has asked, but police said it was too early to say.
An unknown number of families have been contacted, while an unknown number of post-mortem examinations have also been carried out.
Det Ch Insp Jill Johnston said: "This is a complicated and sensitive inquiry which remains at its early stages.
"I understand further arrests might be concerning but I would like to reassure people we have a dedicated team of detectives working on this investigation.
“We are offering support to those families who have had loved ones identified as potentially being involved.
"They are being kept fully updated and supported throughout the process by specially-trained officers."
What has the hospital said?
Boss Wendy Swift last month said "all allegations of this type" are taken "extremely seriously", and said she wanted to "reassure all our patients that all necessary actions are being taken".
She added this afternoon: "We can confirm two further healthcare professionals, who had been suspended following allegations of mistreatment against patients on the stroke unit, have been arrested.
“We take all allegations of this type extremely seriously and when the concerns were raised we immediately contacted the police.
“The trust is continuing to work with the police and co-operate fully with their investigation.
“We would like to reassure all our patients that all necessary actions are being taken. The hospital remains a safe and caring environment for patients and the provision of services will continue as usual.’’
When asked how many patients, if any, are known to have been hurt, and how many families were being contacted, a spokesman previously said there would be no further statement.
What's a post-mortem examination?
Also known as an autopsy, it is an examination of a body after death. The aim is to establish a cause of death.
They are carried out at the request of a coroner because the cause of death is unknown, or following a sudden, violent, or unexpected death, or by a hospital doctor to find out the cause of death, or to further medical research or understanding.
What should you do with useful information?
Police have asked anybody with information that might help their investigation to call 101, quoting log reference 0553 of November 14.
It can also be reported online at mipp.police.uk, which is a police major incident reporting site for the public to use.
The hospital also said concerns can be raised by calling 01253 952270 between 8.30am and 5pm.
Want to tell your story?
If you or your family has been caught up in this investigation, you can call our newsdesk in confidence on 01253 361733.