I still have no idea whether on your account perceiving some system as comprised of four things requires some ontologically distinct noncomputational something-or-other in the same way that perceiving a system as red does.

Aha! Only now do I understand exactly what you were asking.

Recap: I complain that colors, such as redness, exist in reality, but not in physics as we describe it now, not even in the physics of the brain. So I just postulate that somewhere in the brain are entities, "manifolds of qualia", which will have a naturalistic, mathematical description as physical degres of freedom, but which in their full ontological reality are actually red.

So great, I've "saved the phenomenon", my ontology contains true color. But now I need an ontological account of awareness of color. Reality contains awareness of redness, just as much as it contains redness. This is why I started talking about "positing" and "givenness" and the subjective pole of intentionality - because that stuff is needed in order to say what awareness is.

The question about fourness starts out looking simpler than that. If you asked, Does your ontology contain redness, I can say, Yes; it contains qualia-manifolds, and they can be genuinely red. The question about fourness seems quite analogous. If there is a square in your visual field, do I claim that there is a platonic property of fourness inhabiting your manifold of visual qualia?

I believe in the existence of colors, but I am a skeptic about the existence of numbers. You might get away with a metaphysics in which there are no number-entities, just states of processes for counting. I'm not sure; if numbers are real, they might be properties of collections... but I'm a skeptic.

More importantly, my ontology of conscious states gives redness and fourness a different status, which allows me to be agnostic about whether or not there's a real "essence of fourness" inhabiting the visual sensation of a square. I hypothesize that the entity "redness" (more precisely, a particular shade of redness) is itself part of the entity, "awareness of that shade of redness"; but that "awareness of fourness" does not contain any correspondingly real "fourness". Analysed, it would be more like "awareness of a group of lines to which the concept of fourness is posited to apply", or perhaps "awareness of a group of lines together with the awareness that they are being categorized as a foursome by your nervous system". I'm willing to countenance a functionalist account of number "perception", but not of color perception.

I hope that this answer, if not intellectually satisfying, at least addresses the question. And now, back to work for a few days...