Closed private tournament
OK, and then what?
All you have to do is start a group and get only those people to join. Then you could have a private tournament.
I think you have to be a paying member to start your own group. I may be wrong though.
But even if you're unable / unwilling to do this, it's easy. Just put a sign up sheet / email at your company. After people join do the pairings yourself, play the games on chess.com, and keep track of the results through email, just for example.