There are several different solution available for thermocouple amplification such as the MAX31856, AD8495, and LTC2983. Some of these support grounded thermocouples (AD8495) and some don't (MAX31856). This is not explicitly stated in the datasheets. How can I tell? My best guess is that I needs to look for a common-mode voltage rejection down to 0V. Is this correct?
Below is a picture of a "grounded thermocouple" configuration.