While I’m here:
My original thought that started all this wasn’t about trios, but was about a technique I’d heard Bowie and Eno did back in Berlin. My wife just pointed out 10 Jan is the anniversary of Bowie’s death, which is a curious little coincidence.
Apocryphally, say, Eno would lay down one track of music, then go away. Bowie would add a second track, then fade down Eno’s. Eno would come back and add a new layer, responding to Bowie’s track, then fade out Bowie’s. Repeat, repeat, repeat, each person always only hearing the last thing the other person did, until perhaps there’s 20 tracks. Then they’d come back together and explore the different combinations of tracks and see where the magic happened…
This idea somehow morphed into this quite different LCRP concept, but maybe there’s something in there that might inspire you, either for this or elsewhere.
One of the trios I’m in is talking about sharing multiple takes or ideas - i.e. person one will send on 5 things, which the next person can then pick from. Despite being the one who came up with the above concept, where I’d been thinking you pass on one mixed down file, I found this a great relief. 
We’re also talking about doing multiple passes - working fast and seeing if we can do e.g. six layers, nine layers, etc.
I’m going to crack the whip on sticking to time, but hopefully it’s coming through loud and clear that other than that (and sticking to a trio) no one is policing how you do what you do.
