Isn't that 3 contributor limit just a virtual limit.
Assume there are 5 contributors (A, B, C, D, E) for a project. The organization could do this:
1. Create two private copies of that repository
2. A, B, C contribute to the first repository
3. C, D, E contribute to the second repository.
4. C will maintain the synchronization
5. One could write scripts for performing synchronization.