Investigations are continuing into two separate incidents in Toryglen when wheelie bins were set alight.
And in two similar incidents, an elderly couple had to leave their home in Cathcart and a couple had to be treated for smoke inhalation in Pollokshields.
In the first incident in Toryglen, a six-month-old baby was taken to hospital and in the second, two women had to be moved to temporary accommodation due to extensive damage at their block.
The estimated repair bill to both blocks, run by Thistle Housing Association, is £130,000.
Fire broke out on Saturday, April 28, around 1.30am in Edinbeg Avenue, causing around £100,000 of damage.
Wheelie bins were dragged into the common close and set on fire.
Several people were evacuated from their homes, including two pensioners in their 80s.
Both women suffered smoke inhalation and were taken to the Victoria Infirmary for treatment.
The pensioners homes were extensively damaged and they are now in temporary accommodation.
Other residents had to escape via scaffolding as they were unable to get out through the close.
An earlier incident, on Friday, April 6 saw wheelie bins set on fire at the rear of flats in Prospecthill Road, around 5.30am.
The fire spread to the common close and the doors of the flats inside were damaged.
Around £30,000 of damage was caused.
Both blocks of flats share the same communal back court on Prospecthill Road.
Detective Constable Ainsley Stewart, of Cathcart CID, said: "I believe this was a deliberate attempt to cause serious damage to the homes in the flats involved.
"Whoever did this had absolutely no regard for the residents.
"Most people who live there are elderly and would have found it difficult to get out of the house without help."
Grace McColgan, director of Thistle Housing, said: "Our primary concern is for the safety of the residents in the area.
"We are urging residents to remain vigilant."
Elsewhere, an elderly couple were forced to flee their Cathcart home last Friday following a deliberate wheelie bin fire in their basement.
Police said the man, 84, and his 83-year-old wife were woken when they heard a loud noise in their kitchen at Old Castle Road.
They found the room was on fire and managed to get out of the house.
In another incident, a couple discovered a fire at their front door in St Andrews Drive, Pollokshields.
The man, 43, and his 28-year-old partner, found the fire at about 4pm on Friday.
They were treated in hospital for smoke inhalation.
Anyone with information should call police on 0141 532 5400.