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!
One thing that was kinda cool was that Github's interview process isn't necessarily so technical, because they usually find out if someone is a good programmer by just looking at their Github, and having popular repos sometimes catches their attention. Also, all new employees push to the master Github branch on their first day IIRC.
Cheers!