You can increase the size of your storage capacity by purchasing more storage-related furniture (shelves, wardrobes and chests) from the shop or by upgrading them.
You can access the shop by tapping the shop icon on the left navigation bar (orange anvil shield icon). Select the ‘Storage’ filter docked on the lower part of the screen to access all of the storage-related furniture available for purchase. If you’ve reached your max furniture count select an existing piece of storage furniture and upgrade it for no additional furniture point cost.
Upgrading your storage will increase the amount of aritfacts you can keep in your inventory.