One pilot plus emergency provisions, take two(+?) back down.
And you have to know you have a serious problem in the first place. It may well be that missing tiles weren't the primary cause anyway.
Can the Soyuz and shuttle dock? I've not heard of that. There is a docking adaptor for the ISS and they had one for the Mir, but not the Soyuz. In any case, the shuttle didn't have a docking device for anything on this mission. That means an open space transfer unless the Soyuz could be rigged with a docking device on short notice. They had no EVA suits, and, as far as I know, no tethers. The Soyuz would have to bring the EVA gear and teathers, otherwise you're talking about jury-rigging an open space transfer in flight suits. Could they even re-pressurize the cabin after the transfer? You can do that if you plan for EVA and have an airlock and reserve atmosphere that you can afford to vent and purge.
And you have to know you have a serious problem in the first place. It may well be that missing tiles weren't the primary cause anyway.
When this happened my initial thought was a control system problem. But you wouldn't know that until you did the de-orbit burn and got down into the maneuvering at re-entry, and by then you're comitted to landing. Not much could be done then except work the problem as best you could, and if you get out of trim at Mach 18 or so its going to be hard to avoid going into a tumble.