It depends on which chapter of the Meditations we are focused on. What’s in the second meditation is merely that one cannot doubt their own existence, since the very doubting necessitates that one exists. In this regard, even a person with DID won’t affect this, since as each alter fronts and performs Cartesian Doubt, that alter finds that they exist.
The problem of course is with what Descartes does later, in (1) assuming that introspection is in a sense infallible and (2) the ego in the cogito is absolutely simple (3) Thus, the cogito is the activity of a simple thinking substance (res cogitans). DID destroys both premises pretty clearly.
The whole function of disassociation and repression from and of traumatic experiences is to protect the psyche. The cost is a defect not only to one’s introspective access to prior mental states, but confusion on how to interpret current mental states. The very mechanisms involved in DID show (1) is simply false.
It gets worse though. DID also exhibits that the self is no simple entity, contrary to the Cartesian claim (psychologically). DID happens not because one has a traumatic experience that “cracks the ego” but rather because young children (before the age of six) don’t have a fully formed ego to begin with. As they disassociate under extreme trauma, the lack of a fully formed self means these fragments of experience can acquire their own egos (and become alters). It’s why DID is not professionally diagnosed for traumas outside of early childhood and for one time traumas.
What is taken to be simple in the cogito by Descartes, the "I" or "ego," is not only not a simple unity, but its emergence within all humans (not just those with DID) is a complex process of various ego-states fully integrating and fusing since infancy. The Structural Theory of Dissociation while not uncontested, is becoming quite standard in the literature on not just DID, but PTSD as well. The "ego" of even each alter in DID is no simple unity, but is the amalgamation of countless ego-states in the first six to eight years of life. There is no psychological simplicity of the ego, period. The Cartesian argument flows from unsubstantiated premises (1) introspection is infallible and (2) the I or ego is simple (which the lack of simplicity of the cogito flows from the lack of simplicity of the ego).
Without support from premises (1) and (2), Descartes cannot infer his conclusion, whether in regard to a singlet having one res cogitans wedded to their body, or a system having multiple res cogitans wedded to their body. DID removes all support from (1) and (2).
The “ego cogito” is no simple thing. It not only is absent at birth, but doesn’t fully congeal until about six to eight years old. So, Cartesian speculation about the soul is unwarranted (though not falsified) by what we understand of DID today.