This is an article from 2011 that does a good job of summarizing some of the research available to that point around DID, memory formation, and treatment:
Dissociative Identity Disorder: Overview and Current Research
Some useful quotes (all bolding added for emphasis)
Because of the intense feelings experienced as a result of trauma, individuals with DID may behave in ways that facilitate exploitation or are dangerous to themselves or others. Thus, a primary goal for treatment is to manage these behaviors and teach impulse control with some form of cognitive or behavioral therapy. Even when amnesia exists between alters, therapists should hold the client responsible for behaviors of all alters. Therapists should also realize that some clients do not desire fusion or integration of their personalities. In this case, the goal of treatment would involve working towards cooperative functioning of alters.
The thing to notice here is the terminology - fusion I take to describe merging, integration to describe co-consciousness, and co-operative functioning to describe something that relates more to co-awareness; acknowledgement without necessarily sharing consciousness.
Other studies have discovered findings that are relevant to the relationship between trauma and memory in DID. A case study investigating the neural correlates of switching between alters used functional magnetic resonance imaging to study changes in the brain during switching. The results indicated that during switching to the alternate personality, the client’s bilateral hippocampus was inhibited, as well as the right parahippocampal gyrus, right medial temporal lobe, globus pallidus, and substantia nigra. However, during transition to the host personality, the right hippocampus demonstrated evidence of increased activation, with no inhibition in any brain structures (Tsai, Condi, Wu, & Chang, 1999). These findings contribute to an understanding of amnesia between alters, since regions of the brain involved in memory are either inhibited or activated.
Support for the factual understanding of lack of co-consciousness is indirectly an explanation for what co-consciousness itself is.
Other research supports the idea that alters develop to protect the host from unpleasant thoughts and memories involving trauma and abuse. Autobiographical memories may differ between alter personalities, allowing the host to retain positive memories while alters contain negative traumatic memories (Bryant, 2005).
A study investigating directed forgetting found that “dissociative patients showed directed forgetting between states, but not within the same identity state” (p. 241). This study clarifies the mechanism and function of memory in various dissociative states and helps explain why trauma might result in the
development of alters.
Pushing threatening material out of consciousness can then be facilitated by a switch from one state of consciousness to another (Elzinga, Phaf, Ardon, & van Dyck, 2003).
Bear in mind, these are studies that support hypotheses, using a very limited data set. However, that's where much of mental health research is right now.
I also recommend reading this study:
Dissociative Identity Disorder: A Controversial Diagnosis, which is rather dense, but gets more into investigating trauma, memory, personality formation, and traumatic amnesia.
This study is a very important read, I think, in terms of looking at the data that challenges dissociative amnesia across DID identities:
Inter-Identity Autobiographical Amnesia in Patients with Dissociative Identity Disorder
While it does not state anything other than an inability to prove true lack of co-consciousness (and inability to prove does not mean it doesn't exist), it delves deeper into the specifics of how traumatic memory works in an integrative way, and illustrates how to think about memory in some interesting ways as well.
From the study:
Indicating that autobiographical memory might be a prerequisite for compartmentalization, two case studies directly addressed autobiographical memory performance in DID, and both provided evidence for autobiographical amnesia. To illustrate, Bryant examined a 31-year old DID patient in two conditions: As the predominant (“host”) identity of the DID patient, and as a nine-year-old trauma identity claiming awareness of abuse of which the host identity was unaware...Although the data from the two case studies suggest autobiographical amnesia in DID, they have important shortcomings. First, that one identity does not report certain memories does not necessarily mean that these memories are truly inaccessible. Failing to mention a memory does not necessarily mean that the person is unable to recall it. True amnesia would entail an inability to recall these memories, whereas unwillingness might suggest malingering or factitious behavior. Second, each study examined only a single DID patient.
At the very least, our data are inconsistent with the definition of dissociative amnesia in DID as entailing separate inter-identity memory systems divided by impermeable amnesic barriers. The DID patients exhibited memory transfer across identities even though they did not realize it.
Which suggests that it's possible that achieving co-consciousness means nothing more than realizing (identifying) information that is already present.
These are very fine distinctions. But, if you are looking for a more detailed analysis/understanding of the dissociative event itself, traumatic memory, and what is and is not understood fully in terms of scientific studies...these links should help at least get you started.
You will not find anything that presumes the term co-consciousness, I don't think - that's a concept adopted by the dissociative identity community as a way to describe awareness/non-awareness in alter states. Studies will only talk about memory, memory retrieval, autobiographical memory vs neutral memory, traumatic amnesia, and identity states. Even the term 'alter' is not as commonly found inside the research. 'Alternate identity states' will yield you more search results than 'alternate personalities', in terms of search queries for info on DID studies.