Three prisoners have died within 11 days of each other at HMP Woodhill prison in Milton Keynes.
Inmate Mr Culverhouse, 29, died in hospital on 29 April while Mr Green, 53, and Mr Iverson, 51, died in custody on 30 April and 9 May respectively.
The Ministry of Justice said: "The Prisons and Probation Ombudsman will hold independent investigations."
HMP Woodhill prison was found guilty of 'systemic failings' in January this year over suicide of young inmate in 2015.
23-year-old Ryan Harvey, who had a learning disability and was classed as a vulnerable adult, was the eighth in a series of 18 self-inflicted deaths at HMP Woodhill over a three year period (2013-2016).
He took his own life just days after arriving at the prison.
During an inquest into his death concluded that multiple failings by HMP Woodhill led to Ryan’s death.
The inquest jury found staff failed to remove a ligature from Ryan’s cell after he had used it in a previous bid to take his own life.
Jurors said a number of systemic failures and repeated failures to share “critical” information had contributed to the death.