Amanda
We had tried to get a booking at the Chef's Table for 2 previous trips before we finally landed an evening for our visit this January. All I can say is keep trying for this trip, and for future trips make the calls early. I called in July for possible nights in January, and only 1 evening was available, which I grabbed.
The entire evening is remarkable, well worth the wait and the cost. Your party, and no one else, is at the table, and the food, atmosphere, service, and interaction with the Chef's is a once in a lifetime event. The fact that it's you and your party is an important part of the evening, so I'd be very surprised if a group would be willing to add others.
In our case 4 hours and 13 courses!
Good luck.