Proposal: Sell a wearable "pet harness" to which you can attach all your pet summoning devices. The harness will take up one inventory slot wherever it's worn, but the other devices attached to it will not take up an inventory slot, and each device can be accessed while in the harness.

There are many pets in the game at this point, each with its own home that can be worn: kitten slings, puppy cages, fox bugles, dragonfly morning glories, rat sacks, hedgehog pouches, phoenix spheres, wisp amulets, sand elemental shards, leech jars, fishie sacks, wermths, and more. Some, but not all, of these can be accessed to a limited extent without being worn, but most must be worn to access all their features.

This not only results in a lot of clutter in your inventory, but also takes up valuable inventory slots. In fact it's impossible to fit them all, and you are forced to rotate them on and off your body to interact with different pets, which can be a cumbersome process. Allowing all these items to be attached to a common item would alleviate this problem.