I’m fascinated by the idea of chimeras, which happens when twins become one person in utero very early on in the pregnancy. According to Wikipedia, “For example, the chimera may have a liver composed of cells with one set of chromosomes and have a kidney composed of cells with a second set of chromosomes. This has occurred in humans, and at one time was thought to be extremely rare, though more recent evidence suggests that it is not as rare as previously believed. Most will go through life without realizing they are chimeras. The difference in phenotypes may be subtle (e.g., having a hitchhiker's thumb and a straight thumb, eyes of slightly different colors, differential hair growth on opposite sides of the body, etc) or completely undetectable .”
Go here and start about 4.5 minutes in to hear about a woman who discovered she was a chimera when she was told DNA tests showed she was not related to her sons.