The size of the Sack of Sacks can be also increased by upgrading it in the Account & Profile Upgrades section of Elizabeth's menu. Each upgrade adds additional 2 slots to the Sack of Sacks. The costs and upgrade times are following:
One can upgrade the Sack of Sacks with the Account & Profile Upgrades even before obtaining it at all, although it still cannot be used until it is unlocked (a message will appear on the lore of the upgrade item saying that one hasn't unlocked that feature yet).
Multiple sacks of the same type can be placed into the Sack of Sacks.