On paper, connecting one side of each thermocouple to ground looks great. Heck, now you can connect eight of them instead of just 4. There are, however, some serious side effects. First of all, do you know what ground is? Unless you are lucky enough to have a large diameter copper rod driven in the earth inside your lab (I am), then you are relying on the ground of your USB-6009 which is influenced by the ground of your computer, which then plugs into the wall. The potential of this "ground" can vary my 10s to sometimes 100s of mV and contain an assorted array of random spikes. If you are measuring a 1V signal, no problem, but for a thermocouple you are in big trouble. Next problem is noise pickup. In a single-ended configuration the two signal paths are different because your ground runs everywhere. This unbalanced configuration acts like an antenna, and your temperature signal will be lost in either a forest of 50/60 Hz and their harmonics as well as your local AM station. Finally, you are probably tempted to run a single BNC cable to each thermocouple. Now the outer conductor is both a shield and a signal wire. As a shield, the potential of the outer conductor will be fluctuating, and due to the capacitance between the two conductors, your signal level will also fluctuate. Much better with shielded twisted pair and differential measurements.
In short, measuring 1V signals with cables less than a couple of meters long, go single-ended. Measuring smaller signals with longer cables, go differential. Switches and/or multiplexors aren't terribly expensive.
