I'm running into a similiar issue.
I've been able to dres a character in stacked clothing, export the avatar and enable and disable clothing item game objects within Unity.
To do this you need to get around the in CC3 tagging system that generally limits one shirt or shoes or pants at a time, by assigning the item and resetting the tag using "Transfer Skin Weights" and using the setting "Other". That way I've been able to stack a bunch of outfits. For Hair, I've generally had to "Convert to an Accessory".
However, there seems to be an arbitrary and not always consistent Limit to how many items you can get with this approach. I realized after an hour of frustration that at a certain point, adding a new layer would delete an existing item to "make room" in the hierarchy of clothes.
If anybody from RL could speak to what the limit on simultaneous items might be that would be glorious.
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