There are several potential schemes for connecting several thermocouple probes to a single microcontroller or host board. The first consideration is the digital interface used to transfer data. Maxim's thermocouple-to-digital converters feature either an SPI-compatible interface or a 1-Wire interface.
While SPI is very common and easy to use, Maxim's thermocouple-to-digital chips are not daisy-chainable so it does require a separate chip select pin for each IC used. An analog multiplexer can be used to multiplex several thermocouple probes onto a single thermocouple-to-digital converter IC, but this adds a small error to the measurement and additional control circuitry to enable the multiplexer channels. The MAX31855 is an SPI-compatible thermocouple-to-digital converter.
With the 1-Wire interface, many thermocouple-to-digital ICs can be connected to the same 1-Wire bus. Each device has a unique 1-Wire address, so it can be easily selected for read back with no additional hardware. All thermocouples would occupy only one pin of the master controller. However, implementing a 1-Wire master interface is challenging. While there are online resources to do it, there is another option - the I2C to 1-Wire bridge chip. Using the DS2484 or DS2482-xxx chips, the master device can control any 1-Wire bus through standard I2C commands. The MAX31850 is a 1-Wire thermocouple-to-digital converter.