Police Scotland and the Health and Safety Executive (HSE) are carrying out a joint initial investigation into the deaths at Pentland Hill nursing home in Edinburgh.
Care standards watchdog the Care Inspectorate is also looking at four separate complaints about quality of care which are unrelated to the police inquiry.
It emerged in August that police are investigating the death of a 67-year-old resident at the Bupa-run home the previous month.
A damning report by the Care Inspectorate also led to the suspension of new admissions to the home.
Inspectors raised "serious concerns" about the quality of care there following a significant number of complaints in the last year.
They carried out an unannounced review in July after upholding three complaints from families of residents in the past year.
Inspectors found problems with the quality of care and with the management of the home in Gylemuir Road.
They issued a formal improvement notice and new admissions were suspended. That suspension will remain until the inspectorate is satisfied that the quality of care has improved.
In the latest statement on the care home, a police spokesman said: "Police Scotland and HSE are carrying out a joint initial investigation in relation to four deaths. In addition the Care Inspectorate is also investigating four complaints that are not related to the Police Scotland/HSE inquiries."
A spokesman for the inspectorate said: "Every person is entitled to high-quality care which reflects their needs and promotes their rights. We are continuing to support this care home to make the urgent changes we set out in our improvement notice. We are now assessing the extent to which these requirements have been met.
"At all times, the health, safety and well-being of the residents is our top priority, and we continue to work closely with other agencies."
Vivienne Birch, director of partnerships at Bupa Care Services, said: "We always report any issues, however rare, to the police and relevant authorities and, as in these cases, we actively support their investigations.
"The home had reported all injuries and admissions to hospital to the Care Inspectorate and social services."