This situation is called SUPERFETATION and is a very rare occurrence and thought to be much more common with in vitro fertilization (IVF).
This most commonly happens by accident since the human body generally prevents the release of more than one egg at a time for fertilization.
This is different than carrying identical or fraternal twins. In the case of identical twins, one egg is fertilized by one sperm and then this one fertilized egg splits and develops into two babies. With fraternal twins, two eggs are released during the same cycle and fertilized by two different sperm.
In the case of superfetation, the release of a second egg is delayed and may happen weeks after the fertilization of the first egg. THEREFORE, you can actually get pregnant again even though you are already pregnant!!!!
So, this is not actually an urban legend since there is a picture of two babies, one black and one white in William’s Obstetrics showing that this can occur.
Interestingly, just like with superfetation, even in cases of fraternal twins, it is possible to have two fathers for each of the twins if the patient has been having sex with more than one male partner.