Okay, here are my thoughts...
I'd actually argue, despite those postmodernists who would call "The Self" a fiction or a discourse, that The Self (no quotes) has the same ontological reality as a tornado, a coffee cup, or inner city riot. What I mean by this is that all three objects (and as a speculative realist I'm interested in objects) are emergent from deeper multiplicities. A tornado emerges from multiplicities of air, moisture, pressure, and heat. A coffee cup emerges from multiplicities of molecules, physical forces and chemical interactions. A inner city riot emerges from multiplicities of human individuals, social pressures, and government force.
Likewise, The Self emerges from a multiplicity of storytelling, competing desires, and alternate personalities, yet just like a tornado, a coffee cup, or an inner city riot, it is an object - a single object that is as real as anything else we would name with a singular noun.