I got the server plugin found here: https://github.com/Boulldog0/UltimateBackpack/

It adds backpacks that are GUIs opened by clicking a designated player-head that takes up a spot in your normal inventory. (almost like curse of binding).

I'm not sure if the these events are only server side or if you can catch them from the client too: "BackpackItemAddEvent & BackpackItemRemoveEvent".

Maybe GUIs are a bit too much. All there is a fat chance such capability also would all other GUIs on a server that you don't want.
(for example a warp menu or a Auction House menu, those items are not yours.)

But if it was possible, probably you would need a manual interaction where you click a button to add that backpack to memory.