I found CN0354, which uses the ADG1609 multiplexer to read from 4 different thermocouples. Would ADG726 work as well for 16 thermocouples? A short examination of the specs makes them look functionally very similar.
In CN0354 the ADG1609 is operating using a +/-5V supply. The ADG726 cannot operate with these supplies, the maximum dual supply is can operate with +/- 2.5V.
Maybe using multiple ADG1609 is an option?