A man is being questioned over the murders of a clergyman killed at his vicarage and a pensioner stabbed to death at her home.
Stephen Farrow, 47, remains in custody after Avon and Somerset officers were granted a further warrant of detention to hold him for an additional 36 hours.
Farrow was arrested in Folkestone, Kent, on Sunday on suspicion of murdering Mr Suddards after police launched a nationwide manhunt.
Mr Suddards, 59, was found stabbed to death at his home in Thornbury, South Gloucestershire, on February 14.
Farrow was later arrested on suspicion of murdering retired teacher Betty Yates, 77, who was knifed to death at her cottage in Bewdley, Worcestershire, on January 2.
An Avon and Somerset Police spokeswoman said: "Police have obtained a further warrant of detention in relation to the 47-year-old man currently in custody. This warrant is for an additional 36 hours. This takes us until the early hours of Wednesday morning."
The custody extension will be used to quiz Farrow over the deaths of both Mrs Yates and Mr Suddards, Avon and Somerset police confirmed.
Mr Suddards's body was found by workmen who had arrived at the vicarage next to St Mary's Church in Castle Street. The news of his death sent shockwaves through the clergy and the close-knit community, 11 miles north of Bristol.
News of the 36-hour extension to quiz Farrow came as parishioners were to hold a private candlelight vigil at St Mary's Church to remember Mr Suddards.
Mrs Yates was found dead at the bottom of stairs at her home on the banks of the River Severn on January 4, having been killed two days earlier. West Mercia officers investigating her killing arrested and questioned a man on February 2 before he was released on bail.