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I agree with Merchant's stance on Abstract Existence.
Regarding Higher-Dimensional Existence, I think it should apply to Eru and the Ainur (in their origin), as the language implies Eru's "reality" to be higher than the Legendarium ("Primary Reality" vs "Secondary Reality" as well as language saying that the movement of the Ainur into the LOTR univerese was a "descent/descension").
Plus we already have Eru as 5-D for having the Legendarium be fiction to him.