I've got a few variations depending on what would work balance-wise:
1) Using advanced bagpacking techniques you are able to pack more things inside bags/containers. So Bigger Bags might be able to store 20 items, etc. Perhaps not all types of containers would qualify (such as the elemental pouch)
2) You would be able to put specific item bags inside the generic bags/bigger bags. You would not be able to open (or put things inside) containers inside bags, of course. Nor would you be able to stick bigger bags inside bigger bags, as that'd just be silly. To help this, it might help to have a dedicated bag holding inventory slot, where you could temporarily put containers, so that you don't pick something up, and could no longer access your containers.
3) The skill would let you use special 'bag bags', bags that are designed to hold bags/containers. There would be a limit as to how many of these bag bags that you could use, and perhaps each one could only hold a few bags. (Say with the first level of the skill, you could only use one, which could only hold four bags)