THIS WAS MADE BY MY GOOD FRIEND, TaxEvasionist, NOT ME. They're the genius behind it. They gave me permission to publish it.

How it works: name one or many item frames to storage and toss them on the ground with a full shulker box.
They will combine and the item frame will retain the nbt data of the shulker box.
Then you can rename the frame to whatever you'd like, once the box is inside it, of course.
Now you have the item frame item that you can store inside of another shulker box.
To get the shulker box out you just place the item frame and then break it. You have to rename the frame to get it to work again after that though.