There are two "sort of" answers to this question. First off, as noted, you can use followers as portable storage. The other option is to put your uncarriables onto a convenient nearby dead body and then use one of the Raise Zombie line of Conjuration spells, recasting as needed.
Edit: on a closer read, you definitely seem to want option two. You can even tell your follower to loot your "Skeever Suitcase" when you're done with it.
Your best possible outcome for this is a follower. However, if one needed an extra container in their house or something, like one next to the alchemy lab etc. It would be best to reanimate a corpse and let it turn to ashes in the spot you need it in. You can store items in the ash pile because they never disappear.
In the Dragonborn DLC, you can obtain a Dremora Butler as a reward from the Black Book: Untold Legends quest. The butler can be summoned at will and will carry your items until you take them back again.
If you use your follower and have them pick up an item, there is no weight limit for them. However, they can't loot bodies, which means that you'll need to loot everything, drop it, and then have them pick it up.