I propose a theory that Elizabeth Afton's soul was split but not among the Funtimes, instead it was split inside of parts of Circus Baby herself.
Basic idea of the theory: part of Elizabeth's soul is in Circus Baby's body and the other is haunting the program. This theory is made to explain why Baby's personality constantly swings from calm to aggressive, especially if we compare the personalities of Circus Baby and Scrap Baby in their UCN voice lines.
The idea is that the animatronic Circus Baby's personality was supposed to resemble Elizabeth's, that's why she says that William made Baby for her. Circus Baby's personality is supposed to be obedient to its creator the same way Elizabeth is obedient to her father but it is supposed to be like a bratty kid the way Elizabeth doesn't always seem to follow her father's rules.
The theory posits, that Circus Baby was made using the Mimic but as we know the Mimic often creates a caricature of a character rather than someone with a personality. Just like that the Mimic turned Elizabeth's obedience into giving William full control of Circus Baby making her follow his commands. And on the other hand mimic gave Circus Baby Elizabeth's brattiness times a hundred turning Circus Baby into a full on aggressive murder robot.
[The "M" in this theory's name stands for Mimic]
This theory makes the timeline go like this:
Elizabeth dies to Baby.
Elizabeth's soul is split putting the part of her that is loyal to her father with the part of Baby that wants to kill and putting the part of Elizabeth that is bratty with the part of Baby that listens to William.
Michael separates those parts by taking Circus Baby's chip out, making her lose the part that does as told to and is a little brat like a child.
Michael thinks he put his sister back together, when in reality he divided her into two.
The part that wants to murder and wants to make her father proud becomes Scrap Baby but then gets burnt and disappears.
The chip, containing the other half of Elizabeth and the other half of Baby, is found and is probably now somewhere waiting to be used as a plot twist in The Modern FNaF Era.