I would have your 10 thermocouples going into 10 pairs of terminal blocks (no special metal needed), then have 5 differential multiplexers feeding these signals into the cold junction temperature compensation circuit then out of this into a single differential ADC. The ADC is going to be the expensive bit, so multiplexing your signal into a single ADC will be simplest and cheapest way of doing it.
Alternatively, if your temperature is not going above 125 degC, use a silicon chip solution or thermistor in a resistive divider then you dont have to worry about cold junction temperature comp