The Federal Government has no say on your particular problem. They do regulate the frequencies which can be used for consumer products, and these devices must comply with FCC rules as to not cause interference on other equipment. (they don't define "interference" as something controlling more than one TV - they just want to make sure the policeman or fireman can talk on their radios and that airplanes don't fall out of the sky).
That being said, some set-top boxes have a couple of code sets available to avoid this issue. You would need to study the owner's manual.
The other thing you need to know is how are these remotes communicating?
1. They could be IR which requires you to point the remote at the equipment. Sometimes this blast of infrared light can bounce off of walls and send the command to another piece of equipment but it's most likely to happen if the equipment is visible from one spot.
2. They could be RF which doesn't need to be pointed at anything and could control equipment in several rooms that are near enough to receive the signal. These are the remotes that would be more likely to have more than one code set available.
If you can't change the remote code set, or if the remotes use IR, your next step would be to install an IR Routing System (Google it) which would be much less expensive than new TVs and set-top boxes.
Other people on this forum could be of more help if you were to provide model numbers for the TVs and for the set-top boxes.