Pokémon Mystery Dungeon Rescue Team DX is littered with things to pick up. The dungeons you will be adventuring in are absolutely packed with assorted berries, potions, and other useful items that you will need. You keep all these in your Toolbox, but your Toolbox has limited space. Eventually, you will run out of the room, and will need to start storing items in the town to make more space.
The good news is that you can increase the size of the Toolbox in Pokémon Mystery Dungeon Rescue Team DX. To do so, you will need to rank up your Rescue Team. Rescue Team rank works a little differently to your Pokémon rank. Each job that you accept from either the post office bulletin board or your mailbox will have a certain amount of team rank that it will reward. This will then be added to your team rank when you successfully complete the rescue.
Ranks are broken up into different levels, starting at Rookie, and as you move through the ranks, you will sometimes get an increase to the size of your toolbox. This is very useful, as carrying as much as you can is very important in the bigger dungeons when you have a lot of quests to do. To rank up fast, just grab as many missions as you can from all sources, and you will rapidly earn lots of team rank.