Twins who literally share a body have different selves, personalities
Do we have individual selves, or is individuality just an illusion? Consider the case of two girls who share one body, Abigail and Brittany Hensel - conjoined twins who, at 18 years of age, are clearly different people even though from the neck down they have only one body. They wanted to make the documentary offered by The Learning Channel so that people would not just stare at them and take pictures. Also here. Here they are as young children.
Most conjoined twins don't live anywhere near as long as Abigail and Brittany. Vital organs may not function properly in a semi-twinned state, and efforts to separate twins may kill one or both. But these girls are consistently separate above the navel and united below.
As their mother says, when she greets them - it is two kisses and one hug. And the future will be most interesting.