How soon after a litter can a cat become pregnant?

Within 6 weeks.

Another Answer

Normally, a Queen comes into heat every two or three weeks, and once she has been mated and had kittens, the heat cycle often starts again as soon as the kittens are weaned. Sometimes, a female cat can become fertile again as soon as the kittens are born.

However, this is far from recommended as letting a cat become pregnant constantly without "resting" her. Letting a cat become pregnant again so soon takes a huge toll on her health and overall quality of life, which then in turn puts any offspring at risk. Unless you are an experienced breeder then the best option is to not even consider having any litters, and get the cat neutered instead.

Additionally, there are so many cats and kittens who need homes, it's not a good idea to bring even more into the world, where finding new homes for the kittens is not guaranteed.