Using the LT1025 to Compensate Multiple Thermocouples

Hello,

I'm working on an analog front-end design for a product that will be sampling multiple thermocouples with a restriction on area of design. I was looking at the LT1025 as it support CJ compensation for a number of TC types. This might be a silly question, but can a single device be used to compensate multiple TCs for multiple instrumentation amplifiers? Should it? A colleague of mine has brought up this as a consideration, and the TCs will all be coming in on the same connector, so on paper, I think this is okay. My concern would be driving multiple instrumentation amps using this part. If anyone has done this before, I'd appreciate their perspective!