I would not follow the tip about connecting multiple thermocouples in parallel. The voltages involved are very small and the Maxim chips are very sensitive to noise.

Source: myself, as I had to put in a diff 10nF capacitor between T+/T- of the 31855 to get good consistent readings. Maxim confirmed this is a known solution and they were supposed to put the recommendation in the datasheet.

So, be careful with those thermocouples.