The Question is, do you really want a "social network" for your startup? If yes, then Why?
There are many tools out there which you can use to connect to your co-founders and co-workers. Like:
* HipChat for private chatrooms.
* Asana or Trello for assigning Tasks and checking on progress.
Or to make things simpler, you can just create a private group on Facebook, and add your team members.
Or to make things simpler, you can just create a private group on Facebook, and add your team members.