The thought that occurred to me after reading that question and the answers it inspired made me think of a jigsaw puzzle - an 'infinite jigsaw puzzle' that goes into infinite dimensions.
Next came the idea that we are each one piece of that jigsaw. Next - you may recall those old wooden jigsaws made of many layers of thin ply - we each have many layers, but each layer is us individually.
So, and this is simply an idea, a very loose hypothesis. We all have one soul which covers an unknown depth of layers, but each of us fits into The Whole. We are each an infinitely tiny fragment of a Giant Spirit beyond our wildest imaginings.
Don't try giving it a name, though - people are liable to go to war over names.