First, thank you for your interest. We have had firsthand experience of this problem ourselves. We're clearly not alone in this. Now about our approach.
As you said tools like Asana are about project management and collaboration on a clear fixed project, xCollabr is more about linking potential collaborators. Which means that, every person in a team can talk about what they're doing and make it available in the scope of say "all the teams in this organization" e.g i can say that i'm currently starting xCollabr and i'll use some A.I. techniques to do this or that. He can do the same for pieces of conversations, pieces of meetings and make them available to a broader audience.
Now teams or organisations as a whole can also tell what they're working on or plan to work on and make it available to say similar organizations in the network.
An example on student organizations :
Undergraduate entrepreneurship club on campus organize a pitch night week 5 of the term.
Later MBA students want to organize a pitch night at week 8 , we can suggest collaboration so that both teams can sync and organize one big pitch night.
This is really a simple example. But it explains well how we go about collaboration differently. No other products provide an interface for teams to form an ecosystem where teams can collaborate with other teams.
Did you check pur mockup/wireframe ? it should also help getting a feel of what it'd look like. https://moqups.com/[email protected]/HbtBvliq
