Have you tried a shared task management app like Asana or Flow? Same premise... applied to note-taking.

I... I still don't get it. I haven't used any of those applications before but I'm assuming it works by different people putting different things in a to-do list and assigning them to members, etc. How does this work in a notebook? Do you assign different part of notes to different people? Do you just come in and work like a wiki without revision history (just removing what others have written and writing your own things in its place)? What does your company actually do?

I can share notebooks in Evernote with people and it Just Works. Where's the pain?

I hope there's more to your app than "I see them type on my screen, and they see me type on their screen".