Ah, good idea! What we’d like it to get the current one moved to another room downstairs, maybe the schoolroom (which would be the dining room if we used the house as planned by the builder). That would get it well away from the stove and the fire.
Then we’d like a separate thermostat upstairs, and the ability to control the ac/furnace from one or the other, as we choose.
Thermostats don't work well together. Each wants to be "the boss". You can make it work out, though, by using a timed thermostat. Once the timer has shut the downstairs thermostat off, the upstairs one can then be the boss. It would need a timer too. They should be on alternate shifts.
As to relocating a thermostat, that depends on from where to where. It is really easy to move to the other side of a wall, but more problematic to move to the other side of the room.
To do it properly usually requires access to the underside of your living space, (basement ceiling).