Over at Modern Muzzleloading a while ago Idaholewis posted a thread detailing exactly what he found necessary to remove all three sizes of Thompson/Center breech plugs.
For the type of long distance target shooting that he does the interior of the breech plug MUST BE free of any manufacturing defects like burrs, screws that are too short/long, etc. He found that only by examining the interior of the plugs with a high end bore scope did he find some of these defects that were causing his accuracy issues. It was necessary to invest in the proper tools in order to reach the inside of the plugs with hand tools so that the defects could be remedied
First, and foremost, is that Thompson/Center never intended for the breech plugs in any of their barrels to be owner serviced.
Therefore, one has to purchase the aftermarket breech plug "wrench" tool off of eBay in 13/16", 15/16", or 1" size that fits snugly around the breech plug. This is nothing more than a thick, rectangular steel plate with a hole machined in its center to match the silhouette of a Thompson Center breech plug.
Second, was a HEAVY DUTY machinists vise. A good one starts at 50 pounds, and they go on up to 100 pounds in weight. The more the vise weighs, the wider the jaws are, and the farther those jaws usually open.
A heavy duty vise REQUIRES an equally HEAVY DUTY bench to bolt it to. A thousand pound bench is not too heavy. Barring a very heavy bench, the bench should be anchored to the floor, if possible. The last thing a person wants is to have his work bench bouncing around the shop floor while he is torquing on something in the vise. Been there. Done that. Got the T-shirt.
As mentioned in some of the other posts in this thread, aluminum barrel blocks in 13/16", 15/16", and 1" octagon are going to be required to protect the barrel's finish from the jaws of the machinists vise, and to provide the most secure grip possible.
Last, but not least Idaholewis invested in a 36" long, forged aluminum pipe wrench. After several years of using a piece of pipe as a breaker bar on a shorter wrench, he decided that spending over a hundred dollars for a lightweight, one piece tool to replace two far less wieldy tools was a LONG OVERDUE investment. It also meant that he could now concentrate on keeping the pipe wrench centered on the breech plug tool, and the breech plug tool centered on the breech plug. Without having to worry about the breaker bar slipping off the shorter wrench.
Finally, there's some kind of break free lubricant to soak the breech plug threads in. Or a small, hand held, steam cleaner to heat the metal up thus expanding the threads prior to the attempt at removal.
Like others have pointed out, UNLESS you feel compelled to remove the percussion patent breech plug from your Thompson/Center rifle (for whatever reason), & UNLESS you are mechanically inclined, & UNLESS you are going to invest in, or already own, the necessary proper tools; it's probably BEST NOT TO TRY REMOVING THE BREECH PLUG. Unless you want to bugger up the finish, and put some really nice scars in the steel of the breech plug & barrel. And, possibly ruin the barrel permanently.