Question: I get confused between the idea of Turiya, the so-called 4th state, which is the Self, and the idea of Turiyatita or beyond the 4th state. How can there be something beyond the Absolute Self, the ‘4th’?

Tom: Turiya means the Self. That is the only reality – there is no real ‘beyond turiya’ (turiyatita). First see how Turiya is defined in the Mandukya Upanishad in verse 7 here.

Then note what Bhagavan Sri Ramana says in Guru Vachaka Kovai verse 567:

567. The difference between the first three dense states and the fourth and fifth states are only for those who are not able to immerse and abide firmly in turiya, which shines piercing through the dark ignorance of sleep.

Sadhu Om’s commentary: The import of this verse is that advanced aspirants should know that all states other than turiya which are mentioned in scriptures [i.e. sleep, waking, dream and turiyatita] are unreal.

Tom: Now see further verses from Guru Vachaka Kovai which explain Sri Ramana Maharshi’s teaching on this subject further:

937. In Jnanis, who have destroyed the ego, the three
     states [waking, dream and sleep], which were seen
     previously, will disappear, and the noble state of
     turiya [the ‘fourth’] will itself shine gloriously in them
     as turiyatita [the state transcending the ‘fourth’].

Tom’s comments: ie. the forth state (Turiya) is in fact Turiyatita – they are one and the same. This is stated more explicitly in the next 2 verses:

938. The state of turiya, which is Self, pure sat-chit, is
     itself the non-dual turiyatita. Know that the three
     states are mere [false] appearances, and that Self is
     the supporting base for them [i.e. the base on which
     they appear and disappear].

939. Is it not only if the other three states [waking, dream and sleep]
     were real that wakeful sleep [jagrat-
     sushupti], the pure Jnana, would be the fourth?
     Since those three states are [found to be] unreal in
     front of turiya, that [turiya] is the only state; know
     [therefore] that it [turiya] is itself turiyatita.

Using much simpler language, I also explain this type of teaching in a slightly different way that you may find helpful here in this video: