Maybe the starting point for this would be if the whole team is involved in the process of vetting the clients and choosing the projects.
If enough people on the team are interested enough to make it work, then they will be motivated enough to please the client, agree to time scales, budget and all that sort of thing.
But, in all honesty, I'm not sure. You would have to be a company that everyone wants to use, so that you would have enough potential clients 'bidding' to be actual clients.
If this was possible, I would love to do it!