I know in the first game there eventually was a dlc that offered a storage so we can save stuff, but i figured with gazillion different items they would have one built in already. I cant seem to find the answer so hoping you guys might have heard or found something already.. Carrying 12 items only is crappy ^ ^. Amazing game tho I want to stay up all night playing it!
The vault in sanctuary is upgradable but you have to buy upgrades with eridium. The claptrap in sanctuary will also give you a small six space storage area. And just to be sure everyone knows the vault is in the crimson raiders HQ.
Never used the underdome storage but everything is in sanctuary. Thebank/vault is in rolands quarters in the HQ and you can access it whenever no fees involved excerpt to upgrade it. You upgrade at black market in sanctuary. Hope that helps.