The biggest issue is cold junction compensation. Most companies do it wrong Measurement Computing just puts a sensor anywhere nearby. It's affected by air currents etc. Totally useless. This
https://www.microdaq.com/measurement-computing-usb-temp-daq.php is NOT the way to do it.
Omega used to distribute a large termination point with a bunch of screw terminals and a buffered temperature readout of cold junction. I ccan't find it now.
I used a relay based multiplexor at one time. Not for computer control. It just paused a few seconds at each point selectable.
Analog Devices made a 4 TC compensator to place on the edge cards of one of their products.
So, it's mostly in the mass of the screw terminals and the need to be in close proximity with a sensor if you want to handle multiple types.