I don't think that there is a way to have more room in your own inventory.
Instead, there are other ways to carry more:
- Build a "donkey train". Attach chests to some donkeys (or mules), mount one of them, then use a lead to pull the others with you. With this method, you can significantly increase your storage slots, with 15 per donkey.
- Use Ender Chests. They act like "cloud storage", meaning that the items you put in one, can also be picked up from another one that's far, far away. Furthermore, what you store in them is private, giving you a world-wide storage available only for you, increasing your storage slots by 27.
- Use Shulker Boxes. They condense a whole chest's worth of storage into one block that cannot be stacked, but can be placed down and picked back up with any tool without dropping their contents.
- Carry your items in "packed" states, like:
- Blocks of ore instead of materials (ores)
- Bones instead of bone meal
- Logs instead of planks
- Etc.
This method may help you to preserve your already existing slots. Sometimes it may help you to make massive slot savings, or sometimes it may be insignificant.