Kind of a weird theoretical situation: how does Torah handle situations with conjoined twins? For example, what about marrying conjoined twins? In my opinion it would depend on what exactly was going on and how they were conjoined, such as situations where there is only one set of sexual organs. I would think a man could marry a conjoined set of twins in the case he was only having sex with one of them.
Conjoined twins situation is unlikely in a perfect Torah world because it would be considered an "Egyptian malady" (Deut. 28:59-61).
Also, there are medical options. At least today.
I guess if I would go completely hypothetical, I think in case of 1 set of organs you can marry them as a normal (one) person. But if there is two sets of organs then the usual laws about marrying siblings apply.
Ex 15:26 is another relevant passage.
I had watched some documentary about a set of twins that they didn't think they could surgically separate, or something like that. Anyway, it's a very rare situation, and I guess the answer would be that one would have to distinguish as to which one he married and which one he did not.
Another odd situation I read about was with a woman whose reproductive system had different DNA than the rest of her body. This was discovered due to a genetic test on her children concluding that she wasn't the mother. A partially absorbed twin I guess. In that situation, I think practically speaking it would still be "her", as it is theoretically her body, though it is an even more unusual situation I think.
Anyway, these are just extreme situations, though probably not as extreme as some of the rabbinic theoretical situations in the Talmud, like when women give birth to animals and stuff like that…
I think Torah identifies problems by external factors (i.e. Deut 23:1). I do not think DNA matters here. If you have a penis you are a male or if you have a vagina you are a female.
So in case of conjoined twins, you have to distinguish which one you marry but it is only in the case of separate sexual organs.