I was thinking along different lines: We get the structure of the explanandum of tocs by psychophysics or psychometrics-style experiments. For such experiments, I was thinking, metaphysics shouldn't make a difference. We just measure structure operationally, so to speak.
If your explanandum is the structural properties of judgments themselves, illusionism has little to say. If it is the structural properties of the thing about which we make judgments, these structural properties being inferred from the judgments...
Then I am not entirely sure to be frank, and I probably need to think about it a bit more, but prima facie I could imagine that a lot of the structure can end up a legitimate part of an appropriately understood explanandum
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