Because I am a stickler for accuracy in language: If they’re a mix, then they aren’t purebred. The word “purebred” means an animal bred from parents of the same breed or variety. Because you have two different breeds involved, they are a mix.
That said…do they go outside? Have you taken a fecal sample to the vet annually? I give heartworm preventative 4x a year – my old man cat doesn’t go outside, and I get annual fecal and blood testing done for him. Get fecals and blood panels done, at the very least, to make sure everything’s good. Without a full picture of your cats’ health, you cannot make an educated decision on how to handle medications and the like.
I was taught, too many years ago, that a seafood heavy diet it not good for male cats. Can cause kidney problems. I have four male cats and I take it very easy on the seafood. Asher is very picky, but when he gets hungry enough he will eat. We’ve had several stand-off’s over canned food. I give him 20 minutes to start eating a new food. Then I take it away and put it out again at the next feeding time. I leave dry food out all the time. Canned is once a day at 8 p.m. He constantly tries to convince me that he’s starving at 7 p.m. and the new food is no good. He’ll even knock the dish on the floor. So far he’s letting me win.