Hundreds and even thousands of fleas, in severe cases, can live on a single dog or cat. There is literally no limit to the amount of fleas that can infest an animal’s skin and hair.
The flea needs to only attain a single blood meal from a host in order to be able to lay about 20 flea eggs on the skin or hair of that animal.
Those eggs soon hatch and become more adult fleas, making the flea population able to expand and replicate quite rapidly.