Cameron Logan, 23, was killed in the fire at his family home on Achray Place, Milngavie, East Dunbartonshire, in the early hours of New Year’s Day.
His girlfriend, Rebecca Williams, 24, known as Bex, is now in a serious condition in hospital after being injured in the blaze.
Police have issued various witness appeals and said a number of people had come forward with information, including individuals who believe they may be the dog walkers sought in earlier appeals.
But officers said they still wanted to speak to anyone else who may have information.
In particular, they are seeking a man in army combat clothing reported to have been walking on the West Highland Way on the morning of the fire.
It is believed he routinely walks from Maryhill to the West Highland Way at Craigton Road, often passing through the Milngavie area, and officers believe he may have information which could help.
Police, who were called to the fire at 7:25am on 1 January, are treating the case as one of murder and attempted murder.
The fire also resulted in Mr Logan’s parents being treated for smoke inhalation and caused the death of the family dog.
Ms Williams, a broadcast journalist with Global Radio, was taken to the Queen Elizabeth University Hospital in Glasgow, initially in a critical condition.
A spokesman for NHS Greater Glasgow said yesterday: “Rebecca’s condition remains serious but stable.”
Ms Williams’ father has said she is “fighting hard” in hospital.
Phillip Williams thanked well-wishers for their support in a response on Facebook.
He said: “Thanks for all the thoughts and wishes. No real change yet but I will try to put up news when I can. She’s fighting hard.”
Ms Williams and Mr Logan had been celebrating Hogmanay and walked home in the early hours of the morning.
Detectives say the fire was set deliberately, resulting in the death of psychology student Mr Logan.
Since then, officers have also been carrying out door-to-door inquires, checking CCTV footage and interviewing people from the party which the couple attended.
Officers were seen searching woodland and waterways near the semi-detached property on Friday. Detective Chief Inspector Paul Livingstone, of the Major Investigation Teams at Govan, thanked those who have already come forward with information.