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Basically, I would like to create an item that is a square that has 4 belt connections on two different sides. 4 belts for input and 4 belts for output. Is that possible?

Object connecting to more than 2 belts, Splitter.

As for your actual question I'd mimic the behavior with loaders and a chest or whatever suits your intended entity function.

It might be possible. We already have an entity called a splitter which is a 2x1 in size, and take accept 2 belts and output one belt. Something like that can be replicated via how current entities are used, or with how some entities created in some mods are used. If someone knows more than me, I'd like to see that answer also.

Hiladdar

Dumb solution: a wide chest with loaders attached. Not a special entity in itself.
https://mods.factorio.com/mod/WideChests

You can also check out Whistle Stop Factories: https://mods.factorio.com/mod/WhistleStopFactories

By default it auto-places loaders under the big machines so they can be belt fed. If there's weird behavior with multiple mods the machine won't be placed, but the loaders will. In that case, mining the loader results in nothing, so you can't get free loaders. Use a 4x4 chest and loaders under it, and you have an entity that *may* do what you want.

Quick test: