Can Conjoined Twins Marry?

I saw the question someone asked about conjoined twins. Indeed, conjoined twins can and do survive to adulthood. One famous pair I’m aware of appear as a two-headed woman who is alive now, 34 years old, and is married. Scientifically, she has the status of two conjoined twins with two separate minds that think independently and with two separate consciousnesses and personalities, while at the same time sharing some lower organs. She is married, but her husband considers himself married to just one of the twins. This woman is not Jewish. Suppose a Jewish two-headed person like this existed. What would be the implications in Jewish law? Would this person be allowed to marry?