I can only speak on Akita’s, since I owned one before. Her AKC name was (LaBrandy-Lady-Bear - “Brandy” for short) but not sure about the Great Pyrenees. (But believe I’ve read nothing but good things about that breed though?) - But Akita’s are indeed known to be quite protective, courageous as well as Loyal, but are indeed also known to be aggressive toward other animals in general. (Especially dogs of the same sex) - They actually recommend Akita’s are best raised alone, with no other pets.
But with that being said… I personally believe that any pup can be raised to be gentle and good with others, regardless of their Breed. (Yes, there are and will be exceptions & sometimes their personalities are going to be just that, theirs. - But that is my honest opinion, and I have owned a load of animals, & not just pups.) I personally feel that their upbringing and how they are raised, has a lot more to do with how they turn out opposed to their general Breed. (I’ve never bought into that, though I do understand when it’s said some Breeds are known to typically have temperaments leaning one way or the other, I still think each has the ability to be either. I have seen both spectrum’s, where Breeds known to be extremely aggressive, are some of the most gentle. And vise-versa, Breed’s known to be great with people and pets, be some of the most aggressive, pain in the ass fur-balls I’ve seen.
Well, not sure how helpful all that might have been to ya? But you might be surprised, all the pups I’ve known to be raised with Cats, all did well with them. (Especially when the cats were in place first) And they were just as protective of them as they would be a sibling. … Hope to get to see this big ole’ pup if you choose to bring him into the family.