Providing that you do not ground any of those T- wires, it is possible to bundle them together at T- pin. However, care must be taken regarding the RON resistance of the mux or switch, as a high RON will affect the voltage drop sensed across the T+/T- terminals for the active cable.
While it is possible to bundle the T- connections, it is recommended to use a two input mux to separate each thermocouple channel in case noise is picked up by one of the cables, as that noise will affect all channels if the T- are connected together.
Wait two full conversion cycles (~200ms Max.) after you change your MUX before reading sensor.