In Dissociative Identity Disorder (DID), it is not possible for two alters (distinct identity states) to take over the body at the same time in the way you described, where different body parts are controlled by different alters simultaneously. DID involves a fragmentation of identity where one alter is in control of the person's body and consciousness at any given time.
When an alter is "in control" or "fronting," they have access to the individual's thoughts, feelings, and motor functions. The transition between different alters, known as "switching," can be abrupt or gradual and is a central feature of DID. During switching, one alter replaces the other as the dominant personality.
While one alter is in control, the other alters may still be present in the background, but they are not actively controlling the body or interacting with the external environment. The experiences of the alters can vary in terms of awareness of each other and the cohesiveness of the system.
It's important to note that DID is a complex and often misunderstood disorder, and the experiences of individuals with DID can be diverse. The way the alters experience their presence within the system can differ from person to person. Treatment for DID often involves helping individuals improve communication and cooperation among the alters and working towards integration, where the various identity states become more cohesive.
Therapy for DID is usually a long and gradual process that focuses on addressing the underlying trauma and providing support for coping with dissociative symptoms. A trusting therapeutic relationship is vital to help individuals with DID work towards healing and a healthier sense of identity.