A minor modification is needed to your stevens 320 - Choate Tool Stevens 320 Magazine Extension Matte

I purchased this item through OP's GunBroker site. It arrived quickly and in great shape. The extension screws perfectly onto my Stevens 320 magazine's threads and the included spring seems appropriate.

One thing I would note is that after installation, the Stevens factory shell follower tends to hang up on the two dimples near the end of the factory mag tube that are designed to keep the follower and factory spring retainer in the magazine when the gun is stripped down. A few times the follower got stuck to the point I had to disassemble the gun to get the follower to go back down the magazine tube.

To overcome this, I simply drilled out the dimples and filed the inside of the factory magazine tube so the follower had nothing to catch on. The holes I drilled are hidden by the bracket that holds the barrel to the magazine, so they cannot be seen. Now this extension works perfectly.