Do conjoined twins have two souls or one? The Catholic position would be useful to know.
This is a pretty popular question on the web 2.0 Internet forums and apparently is still relevant in web 3.0 (or whatever StackExchange is). But the Truths of the Church are still to be found on the old EWTN forums.
In the happy case where you have two distinct persons, you necessarily have two bodies (like Lake Michigan and Lake Superior are two bodies of water)
If two twins are connected physically, we still have two bodies with two individual [sic] persons and, therefore, two souls. There has to be two souls if there are two persons involved. This situation is a mistake of nature, so to speak. So we may assume that at the resurrection of the body the twins will be in an ideal state of existing each on their own.
EWTN Q and A - Dr. Richard Geraghty - 1/23/2004
However, in the sadder case, there are instances where a second body was never formed where there is no concrete evidence that a second human was ever necessarily meant to exist:
A[n unformed] body, even though living but not having a head, is not a human being. So in this situation another human being was not killed.
EWTN Q and A - Dr. Richard Geraghty - 11/17/2007
Still, given the formation of the body or bodies God still has a plan in place, the natural function of twinning didn't fully take place.
Presumably, God would know about the upcoming twinning and would place both souls in the zygote and they would share a body for a time until they are separated [sic]. It certainly shouldn't be problematic to speak of two souls sharing a "body" because we conjoined twins. In essence they have never completed the "twinning" fully to the point of becoming two separate [sic] bodies
Jimmy Akin via Judie Brown - EWTN Q and A - 06/08/2006
You don't lack a soul simply because you were born with half pinky toes (I hope not, I've got half pinky toes). But the opposite can happen too, even in the womb a body can be said to "not exist" because it was consumed (apparently as an act of healing by the rest of the cells)
In other words, the initial zygote can, under the right circumstances, dismiss a cell or group of cells that becomes that second baby (twin.) In the case of an anomaly that also occurs like the conjoined twins, we cannot say that two persons do not exist, but we can say that a circumstance has occurred [sic] which is tragic and, in the particular case you site, deadly.
Judie Brown - EWTN Q and A - 05/06/2002
So, there you have it, conjoined twins have two souls, what they do with them is between them and God.
(just in case you were wondering, the people on EWTN's forum are "Experts" not shmoe's like me)