The correct term is 'line breeding' . Many people who breed rats for pets practice line breeding on occasion. What you would probably want to do is breed them as you described but make sure to keep track of the health of whatever offspring you let live to adulthood. Things that affect rats are myco flareups, other respitory issues, congestive heart failure, mammary tumors and pituitary tumors . Ideally if you see any of these come up, you would want to end that line.

I keep rats as pets only and think you will enjoy keeping your breeders. They are very friendly, intelligent little guys. I have no idea if you have kept rats before, so I hope I'm not insulting your intelligence, but just wanted to say: rats should not be kept on pine or cedar, wire cages are far better than tubs or aquariums (ventilation issues) and as far as keeping them as 'pets', it is recommended that you allot each rat a minimum of 2 cubic feet of space. Find a good quality lab block (I recommend HT) or a good quality senior dog food (protein ~18%) and combine it with a grain mix. They also appreciate fresh veggies daily. If you are so inclined, they are also very easily trained to come to their name and to use a litter box.

Good luck with them! If you want the address of a good pet only rat forum that has a ton of good info on care and housing, let me know.