Hi,

To be honest, I'm not sure what MUX_E1 is supposed to do. There is no need to disable all the CS signals, only to enable the one being used before the clocking starts.
MUX_E1 is the global CS (or enable) whereas A, B, C are the address lines. With this configuration you don't need to modify the SPI code (independent of how many SPI slaves are connected), you just need to set the address lines before you start a SPI transfer.
This is the way I do all my designs.

Your code works but still I have to subtract ambient temperature reading from MAX31855 (TCx) readings to get correct readings
Generally thermocouple is a relative temperature measurement with respect to cold junction temperature. To get the correct temperature of the thermocouple point you need to ADD ambient temperature.
Maybe this already is done in you thermocouple measurement ICs. I didn't read the datasheet, but you should do.

It makes no sense to SUBTRACT ambient temperature.

Klaus