It's confusing, but you are mixing Federal and State laws together. In order to possess a class 3 weapon in MA, you must have a green card and you or a trust or a corporation must purchase the class 3 weapon. You can't upgrade a C&R to take possession of class 3 weapons, but you can get a class 3 weapon shipped directly to your door (and not via a dealer) if you have been approved with a MA Green Card and the ATF has approved the purchase.
So if you want to buy a Class 3 weapon, first get your CLEO to give you a green card. Assuming he/she will approve it, the state will require you to have a C&R (to meet the 'bona fide collector' clause). Once you have your green card, you have to figure out the approach to buy the weapon - either purchase yourself (and your CLEO has to sign off on each purchase) or via a corporation or trust routes (CLEO doesn't signoff on any purchase - only the initial Green Card).
A corporation does not need local CLEO approval to purchase class 3 items. Similar to a trust, a corporation can't seek approval nor can they get fingerprinted, etc. since it's an entity. The primary benefit of a trust/corp is that you keep your purchases to yourself, the ATF and your local dealer. After your first approval, it much faster approval process (vs. an indiviudal) since the ATF skips the background check (a trust/corp doesn't have a record) and they don't have to run fingerprints.
The only thing you have to remember is that you have to keep the corporation alive in order to legally keep possesion of the weapons. If you don't file your annual fee or wish to close the corporation, you have to pay another set of transfer fees (Corp to ATF and you as a buyer to ATF for a total of $400) to move the weapons back to yourself. It's easier with a revokable trust, because you can amend the trust at any time and simply add a family member as a trustee.
When I got into class 3, I created a revokable trust. I'm listed as the trustee of the trust and am therefore authorized to take possession of my weapons. Keep in mind that you will still have to secure your MA green card in order to use your class 3 weapon. The way it works: I'm listed as the trustee on my Form 4 (ATF's Permission to possess) and my Green Card (MA Permission to possess).
Hope this helps - it took me a while to figure out how the process works, but I'm glad I did
