The fires appeared to be growing in severity. That on Friday night caused damage to one corner of the weatherboard villa, which was under renovation, Detective Sergeant Brett Roberts said.
"The other two didn't damage the house."
Police and the Fire Service were called about 4.15am after a neighbour noticed the glow of fire when he looked outside.
It appeared the fire had been lit between 1am and 3am and police wanted to talk to anyone who was in the area during those times, Det Sgt Roberts said.
The first fire at the property occurred when rubbish was piled against the house and set alight and the next two were in trailers parked on the property.
Fire Service Dunedin and East Otago area commander Brendan Nally said a fire investigator had ruled out an electrical fault as the cause of the latest fire.
Three appliances attended the fire. It was described as a "small" fire and the damage was contained to one area of the house.
