I remember the days of actual group builds where my IPMS club would coordinate with a manufacturer (like Revell or Monogram) or a local hobby shop to get the exact same kit for everyone, like a case of Italeri UH-1H Hueys. In my club, the kit was free to the member if you built it.
We would all build the exact same kit, for instance a UH-1H, but other than that, the rules to build it were wide open. Some guys built it straight OOB using kit decals, other guys added aftermarket stuff like PE, cockpit, markings, etc.
One member even converted it into a sci-fi fighter.
Every other month or so members would bring in their builds to show it in progress or to get assistance in some detail or construction.
It was interesting to see all the variations of the same kit. Even modelers who used the kit markings used different marking options. It also gave car or tank modelers incentive to build something different (or vice versa).
Here at FSM, a group build normally goes like this:
"Hey, I just bought the _________(insert latest hot kit name). It is a great looking kit! I am starting a group build today with a ________ theme (insert theme that includes new kit)."
"I am starting a group build thread, anyone is free to join up. The group build badge will be posted in the thread."
I don't see anything wrong with the genre group builds online, but you can try to organize a same kit build. I have seen them successful using very common kits like the Italeri M4A1 Sherman.