
Conjoined twins have been born that share one body, making separation impossible. From the AP story:
A hospital in southwestern China says conjoined twin girls with a single body and two heads have been born at its facility. A staffer surnamed Wang at Suining City Central Hospital in Sichuan province says the girls were born Thursday. Wang said Tuesday the parents, who are farmers, did not want to have the babies at first, fearing they could not afford to keep them alive. She said they transferred the twins to a hospital in the nearby metropolis of Chongqing to be examined by experts. The local Huaxi Metropolis Daily reported the twins weighed 9 pounds (4 kilograms) and measured 20 inches (51 centimeters). They have two spines and two esophaguses and share other organs. Doctors were quoted as saying it would be nearly impossible to separate them.
So, what to do? You can’t kill one for the benefit of the other. So, it seems to me to be the only ethical choice is to raise them as equals. It’s joyfully happened before with less of a conjoining of vital organs. Maybe it can in this case too. See below:

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