"Something like that. She would have said cohabiting, were she coining a term, but she isn't coining the term, so she won't. On Earth, where we come from...if the comment Ophelia - who is not your previous interlocutor; she still needs to pick a decoy name if she's actually expecting this conversation to end up on an alternate Earth's Internet, authored by her own alternate universe hand - if the comment Ophelia heard, about having to leave notes for other halves, is indicative of cohabitation's nature, you would be described as a fully dissociated system; the only thing you share is a body. By contrast, we're most likely what Earth called a median system; it's not inaccurate to say that all of us are present all the time - it's just that we have our own separate areas of concern.
"You were speaking with the one of us who spends the most of our time by far fretting about correctness and seeking to contribute to the accumulation and spread of knowledge, and the implication that what she had spent that much time and effort acquiring was useless in the face of, to our perception, a statement of 'indivisible, apparently-incorporeal, fundamental-to-consciousness souls exist because I said so', hit her right in the pride. She doesn't actually have much of that, so she clings fiercely to what pride she has.
"Also, she does legitimately want to know what happens with traumatic brain injuries here; some possible outcomes would actually potentially disprove the hypothesis that brains store people-data, and, for that matter, be potentially evidentiary for the 'are brains' neural patterns merged, or in superposition, post-cohabitation' question if souls' existing ends up not being parsimonious based on the available evidence; she really wants to find that out, if any way exists to check without personally concussing someone. None of us want to hurt anything - except monsters, and that drive is mostly Diana's alone, anyway. She's outvoted.
"I hope that helps explain what's been happening; while we're thinking of it, might I ask your name? You may call me Sylvia, and I'm sure that if you ask, the science lady will figure out something to call herself once she's driving again."