Search the indicated location to find an inventory slots upgrade. They look like large camping bags, and each one increases your available item slots by four.
1. Search for it near the Cassette Recorder in the Old House, where you manually save the game. There is only one Cassette Recorder in this area, and it is marked on the map.
2. Go up the stairs in the main hall and open the door to the master bedroom after getting the Serpent Key to find it inside.
3. When you first arrive on the Old Ship, there will be a door that requires a fuse to be opened. You have to get the fuse as part of the story to progress further. On the opposite site of the fuse door is a locked door. Behind it is the inventory slots upgrade. You must continue playing the story for quite a while to enter the locked door. Eventually you will get a usable item called Corrosive (which is unmissable and must be obtained as part of the story). You will later have to get back the fuse from earlier to repair an elevator. While you do that, go to the locked door and open it with the Corrosive to get the upgrade.