The good news is setups like what you described don't last long at all. One of the first things you are warned about housing multiple rats together is that if adequate space and food are not provided, they are not above eating their cage mates. Rodent breeding can be tricky if for no other reason than any issue at all will result in cannibalization in a heart beat. I once lost an entire litter of pups because I didn't realize a water nipple had failed, and that was only for a few days. Lesson learned and I check all my plumbing daily now, but it goes to show you that the minimums absolutely have to be met for any measure of success to be achieved. Throwing half a dozen or more fully grown rats in a 10 gallon tank with less than ideal food is a quick way to end up with 2 or 3 very questionably fed rats.