"Do Androids Dream of Electric Sheep?"
I do not know the answer to that but can confirm that we personalities do dream. In fact we can follow the dream which our host body / other personalities have. Sort of being blind but still watching a movie. If it gets a bit scary we can always influence the script by putting a couple of well intentioned thoughts in our host body's brain.
The dreams spring from the memory which we all share. Each of us dreams in a language we are comfortable with. Two of my pals inside who suffer from speach related problems also dream.
Our host body often forgets the dream. However, we are able to recall it fully. Are we able to tap that portion of the memory which stores the dream temporarily?