The term "Shaivite" is overused nowadays. For instance, Iyer Brahmins are often called Shaivites, but they're actually followers of Adi Shankaracharya's Smartha sect (which I discuss here and here), and simply adopt Shiva as their Ishta Devata. True philosophical Shaivism is relatively rare nowadays (in contrast to Vaishnavism which is pretty common). I discussed one genuine Shaivite sect, the Lingayat sect of Basava, in my answer here. But my question is about a more famous sect of Shaivism, known as Shaiva Siddhanta, which is based on the Shaiva Agamas and the poems of the Nayanars just as the Sri Vaishnava sect (of which I'm a member) is based on the Pancharatra Agamas and the poems of the Alwars.
Now in the worldview of the Shaiva Agamas, the hierarchy of gods from lowest to highest is Brahma, Vishnu, Rudra, Maheshwara, Sadashiva. I had initially thought that Sadashiva was considered the supreme being in the Shauva Agamas. But based on my question here and my answers to it, I revised my view and concluded that Para Shiva is considered higher than Sadashiva, and that Para Shiva is the one who's considered supreme, akin to Para Vasudeva in the Pancharatra worldview. But now it seems that even Para Shiva may not be considered supreme. Let me explain.
As I mentioned above, the Shaiva Siddhanta is based on the poems of the Nayanars. One of the most famous Nayanars was Tirumular. In Tantra 8 of his Tirumantiram, Tirumular says this:
Paramparam and Para Maha Sivam
Beyond Para Siva is Paramam;
Beyond Paramam is Paramparam;
Thus are states ascending;
From Para Siva Jagra, to Para Siva Svapna, and to Para Siva Sushupti
The Jiva that has Para Siva become reaches
The Finite Truth that is Para Nandi.
My question is, who are the beings "Paramam" and "Paramparam" whom Tirumular considers to be higher than Para Shiva? And what is the exact distinction between Para Shiva, Paramam, and Paramparam? What are their roles, their nature, etc.?
Are there any Shaiva Siddhanta works that discuss beings higher than Para Shiva? Commentaries on the Tirumantiram may be a good place to look.