A recent note on the network’s Facebook page urged "Please HELP!"
The cats had been cared for by Brockville resident Mary Lockerbie until her recent death.
"The time for Mary’s cats is running out!" the Facebook page said.
"Can you adopt one or two outside kitties or maybe know someone who can?" the network asked.
"All of them are fixed, vaccinated and flea/wormed, timid outside kitties that will be happy to keep your property free of rodents."
It was "incredibly sad" the cats were losing their home.
The house would eventually be sold, and a new home for the cats was needed before then, network organisers said.
Network founder Ana Andrianova said the charity previously helped Ms Lockerbie to look after the cats, and provided advice.
As many as 20 cats may have been on the property, including about four domestic cats and a larger group which lived mainly outside.
A network volunteer who has been feeding cats at the property for the past month said the largest number of cats he had seen there at one time was 15, but that may have included a couple of cats which lived elsewhere in the neighbourhood.
Five of the adult cats had since been rehomed, including two adopted by a network supporter and Dunback Inn Ltd owner Liz Moir. Many of the remaining adult cats at the property were shy and were used to living outside.
Ms Andrianova hoped media coverage would enable the network to "rehome a few more of Mary’s outside kitties to work as rodent control technicians somewhere on lifestyle property or a farm".
If people were willing to take one or two cats on such a property with sheds and barns, that would be "perfect", she said.
Anyone wishing to adopt a cat can contact the network through arnnz.enquiries@gmail.com via internet.
• The network earlier found permanent homes for almost all of about 20 cats and kittens after the death of a North Dunedin woman, Judith Mary Egerton (77), who fed stray cats in the area.
Ms Egerton died after she was hit by a car while walking at the intersection of Dundas and Great King Sts on December 13.
