Once you unlock the first 25 slots in your regular inventory, you will automatically get 5 slots in the Producer Inventory. To get even more slots than that, you need to complete some remarkable milestones. Below is the list of all the goals that will get you to unlock more slots and if you've completed these in the past, they are retroactive and should unlock right away for you. Those are:
- Complete Maintenance Room
- Complete The Pool House
- Complete Plaza
- Complete The Maze
- Complete Conservatory
- Complete Lighthouse
- Complete Hallway
- Complete Heikki's Sauna
- Complete Dining Room
- Complete Landing Room
- Get a Level 12 Gardening Toolbox
- Get a Level 12 Toolbox
- Get a Level 12 Broom Cabinet
- Get a Level 12 Drawer
- Get a Level 12 Mosaic
- Get a White Lotus
- Get a Level 11 Yarn
- Complete the Casey & Skatie Story Event
- Buy all 50 Item Inventory Slots
- Reach Player Level 50
The max amount of Producer Inventory slots is 25.