el8ch is correct.

To add, yes you can do this. Just be sure that all UTHs are exactly the same - same wattage, same brand, etc. And that the total wattage does not exceed the allowed wattage output of the t-stat.

Also, I would put an accurite thermometer (or similar model) in each enclosure to monitor each cage independantly though. Just so you can keep track of what each cage is doing.