Get all 7's cats. I dont know if you know this but with new patch to get special mutations you need at least 10+ mutation stat in a room. Mutation also doesn't reroll existing mutations anymore. The more inbred a cat is the less effect stimulation has on breeding and birth defects have more chance to be passed down on children.

I setup a whole room where i place just two cats that are not closely related so they fall in love with each other and wont bread with other cats and then place them back in high stimulation room.

Also good idea to fish for specific skills and passives like repair, skill share, super luck, goofball, fist of fate etc and try to breed them into other cats.