Multiple personality disorder goes into some strange, unexplained territory. There are case reports where one personality was diabetic, but the others were not, so the personality which is exhibited at any given time can have profound consequences well beyond the mental dimensions. Since those consequences *can* be tied to specific personalities, and only those personalities, I would want to know how the player saw his character. Are the personalities truly separate individuals (one possibility) or fragments of the same personality (essentially only one 'actual' personality but fractured/compartmentalized in order to provide "safe spaces" to adapt to and/or deal with trauma). Ignacia posts above "Justin is a psyche split, caused by trauma. The unnamed one is kind of different. Part of an artifact merged with Adam when he was a baby..." Given that, I would agree with Kileanna and rule that a Dominate Person cast on Justin would also continue with Adam, as at their core they're really still the same person, just fractures of the same personality. But like the real-world diabetic example, I would also rule the third personality would not be impacted (much like Harry Potter might be, but not he-who-must-not-be-named) as this psyche/soul is different that then one the spell was cast on, but as noted be subject to a -6 penalty on any attempt to dominate that one.
Cool question, thanks for sharing!