The animal protection group is seeking to raise money for the second surgery, said Chief Roy Gross.
Gross updated the condition of Midnight, a female mixed breed, who was found with a broken femur, severely underweight and infested with fleas.
Gross said Midnight had surgery to repair the broken bone and is recovering. She now needs more surgery to fix torn ligaments in one of her knees.
The dog's injuries were "caused by blunt force trauma," Dr. Dennis Dougherty, a veterinarian with the Bayport Village Animal Health Center who performed the surgery, told the SCPA.
"This is a very sweet dog and we will do anything we can to see that she gets the proper treatment," Gross said.
Those wishing to make a donation can visit suffolkspca.org or call 631-382-7722.