Turiya is Atman (Soul) the Self itself. From the standpoint of the Atman, the Self, There is no fourth state.+

Turiya is Atman (Soul) 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

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 untruth?” between the dual (waking/dream) and nondual (deep sleep) experiences. All accumulated bookish, scriptural knowledge is not wisdom.

Holding some Guru's teaching as wisdom without verification blocks the realization of the Advaitic truth, which is beyond form, time, and space.

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:~ 

Sage Gaudapada: - The non-dual Atman is realized when the individual self (jiva) is awakened from its ignorance. Atman is unborn, dreamless, sleepless, and motionless; and is beyond duality. It is cognition at its purest. It is Brahman- Ayam Atma Brahma, this Atma is that Brahma; Thus epitomizing the core of Upanishad teachings. 

Sage Gaudapada expands further on these states of consciousness. The Self is AUM. It represents manifest and un-manifest aspects of Brahman. It is the single syllable that symbolizes and embodies Brahman, the Absolute Reality. It is the Pranava that pervades all existence and is our very life-breath. 

Vaisvanara in waking state is the first part of AUM, One, who realizes this, attains his desires.

Teijasa in the dream state is U the second part of AUM. One, who realizes this, attains knowledge. 

Prajna in deep sleep is M the third part of AUM, concluding the sounds of the earlier two parts. One, who realizes this, attains a compressive understanding of all. 

The Syllable AUM in its entirety stands for the fourth state, Turiya the one beyond the phenomenal existence, supremely blissful and non-dual. 

AUM in its integral whole stands for the fourth state which is transcendental, devoid of phenomenal existence; and is the source of all existence. AUM represents the ultimate reality.AUM is thus verily the Self itself. One who realizes this merges into that Self. Meditate on AUM as the Self. : ~ Santthosh Kumaar