How many litters can a dog have per year?
Gestation period (length of pregnancy) is 63 days, then six weeks of nursing, so it could be possible for a dog to become pregnant 3 times a year. But this is so hard on the dog, and can cause serious health problems for her, and for the puppies.
I would never allow my dog to have more than one litter of puppies a year, preferably only every 2 years. A dog needs time for her body to heal after pregnancy, labor and delivery, then nursing, caring for and weaning the puppies. This also results in healthier puppies, too, as well as fewer pregnancy, labor, and delivery complications when she is pregnant.