The other members covered whether or not you could convert a semi-auto Thompson to full-auto. (In short, NO)
However, you *might* have a legal problem with your semi-auto Thompson already, depending on exactly what you have.
You state it's "over 50 years old". Are you SURE of that?
The first semi-auto Thompsons were made in 1926. These "Model of 1927" guns were essentially machine guns with some parts removed so they'd fire semi-auto only. The receivers were the same.
Unfortunately, today these original guns are considered to be machine guns by the ATF, since they use the same MG receiver and can be switched back. (These are the only semi-auto Thompsons made over 50 years ago)
http://www.1927a1.com/
There were less then 50 of these made. If this is what you have, it is rare, but unless it is already registered as a MG with the ATF, it is contraband and not legal to own.
It is more likely that you have one of the more recent semi-auto Thompsons that were first produced starting in 1975. That's not 35 years ago, not 50 though. That's why I asked if you were sure of the age.
Check the barrel length: If your gun has a 10" barrel, you may have a problem. It sounds like you do have either one of the those 50 semi-auto guns that are now considered MG's, or a flat out MG.
If the barrel length is 16", then you have a modern semi-auto version, and all is well.