Yeah. Carter is a wizard / thinker / dreamer, which means his Archetype is the Supreme Archetype. But it is silly to put that as a key for him because ALL wizards, thinkers, artists, dreamers are facets of the Supreme Archetype
Carter becomes one with all infinite possibilites of himself:
"There were “Carters” in settings belonging to every known and suspected age of earth’s history, and to remoter ages of earthly entity transcending knowledge, suspicion, and credibility. “Carters” of forms both human and non-human, vertebrate and invertebrate, conscious and mindless, animal and vegetable. And more, there were “Carters” having nothing in common with earthly life, but moving outrageously amidst backgrounds of other planets and systems and galaxies and cosmic continua. Spores of eternal life drifting from world to world, universe to universe, yet all equally himself."
"In the face of that awful wonder, the quasi-Carter forgot the horror of destroyed individuality."
"Randolph Carter and all his ancestors both human and pre-human, terrestrial and pre-terrestrial; all these were only phases of one ultimate, eternal “Carter” outside space and time"
"He knew that there had been a Randolph Carter of Boston, yet could not be sure whether he—the fragment or facet of an earthly entity beyond the Ultimate Gate—had been that one or some other. His
self had been annihilated; and yet he—if indeed there could, in view of that utter nullity of individual existence, be such a thing as
he—was equally aware of being in some inconceivable way a legion of selves. It was as though his body had been suddenly transformed into one of those many-limbed and many-headed effigies sculptured in Indian temples, and he contemplated the aggregation in a bewildered attempt to discern which was the original and which the additions—if indeed (supremely monstrous thought) there
were any original as distinguished from other embodiments."
"Faced with this realisation, Randolph Carter reeled in the clutch of supreme horror—horror such as had not been hinted even at the climax of that hideous night when two had ventured into an ancient and abhorred necropolis under a waning moon and only one had emerged. No death, no doom, no anguish can arouse the surpassing despair which flows from a loss of
identity. Merging with nothingness is peaceful oblivion; but to be aware of existence and yet to know that one is no longer a definite being distinguished from other beings—that one no longer has a
self—that is the nameless summit of agony and dread."
The fact it's referring to "thinkers, artists dreamers" is due to Quasi Carter being the singularity of all deviations of Carter outside of "space and time" this is perfectly encapsulated here:
"A slight change of angle could turn the student of today into the child of yesterday; could turn Randolph Carter into that wizard Edmund Carter who fled from Salem to the hills behind Arkham in 1692, or that Pickman Carter who in the year 2169 would use strange means in repelling the Mongol hordes from Australia; could turn a human Carter into one of those earlier entities which had dwelt in primal Hyperborea and worshipped black, plastic Tsathoggua after flying down from Kythanil, the double planet that once revolved around Arcturus; could turn a terrestrial Carter to a remotely ancestral and doubtfully shaped dweller on Kythanil itself, or a still remoter creature of trans-galactic Shonhi, or a four-dimensioned gaseous consciousness in an older space-time continuum, or a vegetable brain of the future on a dark radio-active comet of inconceivable orbit—and so on, in the endless cosmic circle."
All things deviate from Carter in some way or form, a mere change making him a
wizard. See it all comes back to Carter. Its not all Wizards, dreamers and thinkers being a deviation of Yog sothoth. They are deviations of Carter, who IS Yog sothoth. All Carters are
all these were only phases of one ultimate, eternal “Carter” outside space and time the eternal "Carter" (the fact its in quotation marks signifies its not TRULY Carter) who is the supreme archetype.
Thus the All in One is Carter. This makes sense because the phrase "All in One, One in All" DIRECTLY CORRELATES with Quasi-Carter's existence. The phrase and his existence are deeply linked.
All variations of Carter are in
One eternal Carter. And that
One eternal carter is representative of
All the Carters.
Conclusion: Overall, for now i believe Carter (Quasi-Carter to be specific) Should get a key for the supreme archetype untill there is evidence provided for the contrary that can poke some holes in the argument. Because as of now all the context, and the explicit statement of Carter's archetype being the Supreme Archetype leads me to that conclusion.