First- there is no such thing as a Class III license.
If you want to OWN a Class III firearm, then (a) possession of that firearm must be allowed by your STATE laws, (b) you must be 21 yrs old, and (c) able to buy an ordinary firearm.
The transfer of that firearm to you must be through a dealer that has a FFL AND has paid the Special Occupational Tax (SOT) to deal in that type of firearm. That dealer can guide you in completing the paperwork, which will include approval from your local Chief Law Enforcement Officer, prints, pictures, the application form, and payment of the transfer tax ($200, or in a few cases, $5)
EACH transfer is treated as a seperate transaction. There is no "Well, I have my license, so you can transfer this one and that one and the one over there, and 2 of those green ones....."
If you want to be a DEALER in class III firearms, that is another matter.