I've also had a female who didn't have pups start producing milk and try to "steal" the pups from their true mother. It was terribly cute watching those puppies with two mothers, especially since they were different breeds.
The "thief" mom would generally nurse five puppies and the "real" mom would only nurse two. The real mom wasn't nearly as good a mom as the thief mom and I could see she was glad for the help. The thief mom nursed the puppies more than their real mom and helped raise them until they were sold.
I would worry about Ceci's swollen, hard nipples though. I'll be curious to hear what the vet has to say about them. Good luck!