The most one can say is that a minimal normative coherence acts as a necessary constraint upon the co-consciousness of conscious contents. Remaining at the personal level and with the subjective components of the account of co-consciousness, Hurley stresses the importance of perspectival consciousness in underwriting the unity of consciousness at a time. Perspectival consciousness is consciousness that reflects the passage through the world of a single subject. It is largely, but not exclusively, perceptual. The idea of having a perspective or a point of view is part of our concept of what it is to be conscious.
Unity is a basic feature of the perspectival aspect of consciousness.
But so is agency. At the personal level, having a perspective means that what you experience and perceive depends systematically on what you do, as well as vice versa. Moreover, it involves your keeping track, even if not in conceptual terms, of the interdependence between what is perceived and what is done, and hence awareness of your own agency. It is concerned directly with how conscious experiences are integrated over time. But it might be used as a partial explanation of co-consciousness.