Different rigs are different rigs, and you're also doubling your memory usage since each rig references a different atlas of the same sprites.
You can, however, use Spine skin functionality to have "different" rigs in the same Spine file. You assign the bones of the first rig to a skin #1, then redo the 2nd rig as skin #2. Then swap skins in the editor and in Unity via code at runtime.
I'm not sure why you need two completely different rigs for the same character, though. The whole point of Spine is reusability, crafting multiple bespoke rigs in separate files for the same character (which is viewed from the same angle) goes against that.
You can also export/import animation data from one rig to another. Import - Spine User Guide: Animation