So, Penric here is already carrying around a disembodied entity bound to his body, Desdemona. Canonically, there is no way to separate them without killing one. (If Pen's body dies, his soul goes to the afterlife and Des jumps to someone in the surroundings[1]; if Des is exorcised, she basically gets returned to the gods and dissolves back into chaos.)

Even though they are two distinct characters because they share a body, Des cannot exist without a host, and we don't canonically see any other human with Des other than a few minutes in the first scene of the book series where Des's prior rider was dying of a heart attack, and Pen happened on her party on the road and offered to help. This is also the only scene with Penric without Desdemona in his mind. (So no chance of ending up with two characters claiming her, even if it wasn't a rare canon.)

Also, assuming this is allowed, how would the locals respond to a non-corporeal being that is occupying a human body, but sharing it, and the subordinate partner in the relationship? Especially since anyone without a perception of magic or souls or something can't clearly tell (anyone who can see magic etc. could tell that there were two beings, and the human who owned the body was in control; otherwise, Penric looks like a normal human).

[1] Which I will assume is blocked, even if the chip is removed, especially since perma-death isn't a thing.