A multiple system is a system in which members are distinct and separate from each other. Due to sharing a brain together, this may not be a complete separation (there may be episodes of mental communication or thought transfer, for example) but it's separate enough for those in the system to consider themselves individuals, distinct from one another. A good analogy for this would be having physically separate people all in a room together- they can talk to each other, and may share certain traits or identities (there may be two people who love to read, for example) but even that is distinct and they view each other and themselves as separate individuals.