Yes, within the context of Dissociative Identity Disorder (DID), it is possible for an alter personality to have its own distinct subpersonalities or "alters inside." This phenomenon is often referred to as "structural dissociation."
Structural dissociation is a concept used to explain the complex organization of identities within a person with DID. It suggests that alters can exist at different levels of awareness and dissociation. Some alters might be more aware of each other and share memories and experiences, while others may have limited or no awareness of other identities in the system.
In some cases, an alter may act as a host or "core" identity, which may be more aware of the other alters within the system and may have a broader understanding of the person's experiences. Inside this host identity, there might be other alters that represent different aspects of the individual's personality or coping strategies, each with its own unique characteristics and memories.
These nested identities can create a complex and dynamic system within a person with DID. Communication and awareness between alters can vary, and some alters may be more dominant or take control of the person's behavior at different times.
It's important to recognize that the experience of DID can be unique to each individual, and the structure and functioning of their alter system can differ significantly. Therapy for DID often involves understanding and working with these different identities to achieve better communication, integration, and healing.