Actually, I think it would be pretty easy to have a project for which none of the existing OSI approved licenses will do without even being all that different, ever since OSI approved AGPLv3.

AGPLv3 contains a distribution requirement that triggers for your program if you have users who are "interacting with it remotely through a computer network".

Now all it takes is wanting a license similar to that, but with the trigger being different. Maybe a project agrees with AGPLv3 that if you run their program on your server you should have to give the users source, but wants that to also apply to users who are interacting with it locally on a computer network, or are interacting via some method other than a "computer network" such as serial terminals.