Turiya is Atman, the Self itself. From the standpoint of the Atman, the Self, there is no fourth state.
From the standpoint of Atman, the three states are merely an illusion then the question of the fourth state does not arise.
The Atman, which is present in the form of consciousness alone, is real and eternal.
To realize this truth the seeker has to realize first “What is the truth? and “What is the untruth?” between the dual (waking/dream) and nondual (deep sleep) experiences. All accumulated bookish, scriptural knowledge is not wisdom.
Holding some Gurus' teaching as wisdom without verification blocks the realization of the Advaitic truth, which is beyond form, time, and space.
Remember:~
The Soul, the Self has no name, because it is a formless, timeless, and spaceless existence
The Soul, the Self is present in the form of consciousness. The body, ego, and the world together are the Soul.
Thus, the Soul, the Self is not an individual. The objective observation is dependent on the ego. The Soul, the Self observes both, the objective as well as the subjective.
Objective awareness is unreal and impermanent whereas subjective awareness is real and permanent. Objective awareness is dependent on the Soul, the Self whereas subjective awareness is independent and eternal.
Man and his world are within the objective awareness, which is present in the form of ‘I’. The ‘I’ is an illusion.
Thus, holding ‘I’ as real is holding the illusion as reality without knowing this truth, it is impossible to unfold the mystery of the ‘I’ or mind or universe.
That is why Sage Sankara says: ~ What is accepted without a proper inquiry will not lead to the final Goal. (Commentary on Vedanta Sutra).
Sage Sankara:~ Vc.63: ~ Without knowing and examining the external world, one can’t know the Truth, as the idea that the external world exists, won't go. It can go only by an inquiry into the nature of the external world.
Remember:~
Manduka Upanishad:~Atman is the highest Reality and its opposite: Note the word "and". Reality and illusion together make Brahman: nothing can be left out. Page 51.
Brahman must be realized in the waking state when all objects are present in the form of consciousness, otherwise, it is nonsense. Page 65: v.10.
"Sleep does not exist In Turiya”: This emphatically disproves the mystic use of sleep as an analogy for Brahman. Page 69.
The essential message of Manduka Upanishad is that the whole world, whatever is seen is only imagined. points out that even though it is harder for them, still women can attain Brahman just as men. Page 351
"From their notion": Everybody has his own imagination about facts and starts from that, instead of discarding his personal idea and looking at the fact. Page 333. V. 83:
"Soundless and of infinite sounds"; means both the waking and sleep world must be known, and both objects and non-objects must be understood before the truth of Brahman is realized. Page 96. v. 29
Manduka shows how one opinion may be used to contradict another so that both may be thrown away. Opinions are not for philosophy; they are as Ashtavakra says, mere thoughts; it wants the truth.
In deep sleep and anesthesia, you have non-duality but no Gnana. Therefore there must be discrimination along with non-duality. Otherwise sleeping dogs would be Gnanis. ~ (P.219)
Existence means existence in the sense of the Drik. When you reduce everything to consciousness, Drik, Gnana, or even Mind, giving up all imagination in truth it is unborn. You see a man's body come and go, but that is not the same as seeing him come and go, which you can never do. P.300. V.45.
Sage Goudpada 's 3rd chapter is devoted to proving the existence of Atman in order to distinguish it from the changeable objects in this world, but in the final 4th chapter P.33, verse 83, he discards that position and rejects even the idea of Atmanic existence. He then declares we may assert nothing about it. Not even existence or nonexistence i.e. silence alone is demanded by the truth.:~Santthosh Kumaar