Can I install two thermostats to control one furnace?

Our Monaco does doug. We can use either of them for the furnace or for the AC. For the AC - the AC in the bedroom is controlled with the bedroom thermostat, and the one in the living area controls the AC in the living area. Both thermostats are identical with on/of, heat/AC and a temperature setting and a fan only setting with hi/lo choices. They are Dometic thermostats. We have used either/both for the furnace so we know for a fact that they work that way.