It does look like your Grandpa may register his AKC dog with APRI if the breeder of his dog is in good standing with AKC he could get dual registry. He would need to also send in all documentation to register with APRI. Once he got that then you could register pups with APRI. Sounds like a lot of work. Here is the link I found on your question:
Design Site For America's Pet Registry
From APRI site: "I have an APRI registered dog and an AKC registered dog. Can I breed them and register the litter?
APRI accepts all AKC dog registration certificates at face value if the breeder/owner is in good standing with AKC. The AKC dog can be dual registered with APRI and any litters produced may then be registered with APRI.
Dual registration does not remove the current registration; it merely means the dog is now registered with more than one service. "