Akshar-Purushottam darshan is the youngest branch of Hindu Philosophy. It is based on the teachings of Sri Swaminarayan. Following the tradition, Sadhu Bhadreshdas composed commentaries on Prasthanatrayee (Upanishad, Gita and Brahmasutra) in Sanskrit. Obviously, his commentaries are based on the teachings of Sri Swaminarayan. He was instructed to write these commentaries by his Guru - Pramukh Swami Maharaj, the former president of BAPS Swaminarayan Sanstha. In 2017, Shri Kashi Vidvat Parishad concluded that Sadhu Bhadreshdas is an acharya and Akshar-Purushottam darshan is a distinct philosophical school (link)
In a nutshell, it says the goal of life is to become Aksharrup and offer bhakti to Purushottam. The peculiarity of this school is that it talks about two types of Brahmans - Aksharbrahman and Parabrahman.
To support this division, they quote* the following verses from the Bhagavad Gita.
Dvau imau puruṣau loke kṣaraḥ ca Akṣaraḥ eva ca | Kṣaraḥ sarvāṇi bhūtāni kūṭasthaḥ Akṣaraḥ ucyate ||
There are two types of purush within the world: kshar and Akshar. All those who were and are bound by māyā are said to be kshar, whereas the one who is unchanging – forever beyond māyā – is said to be Akshar (Bhagavad Gitā 15.16)
Uttamaḥ Puruṣaḥ tu anyaḥ Paramātmā iti udāhṛtaḥ | Yasmāt kṣaram atītaḥ aham Akṣarād api ca uttamaḥ | Ataḥ asmi loke Vede ca prathitaḥ Puruṣottamaḥ ||
The supreme purush is distinct; he is called Paramatma. I am superior to kshar and superior to even Akshar. For this reason, I am known as Purushottam within the world and the Vedas (Bhagavad Gitā 15.17–18)
So they conclude that Bhagavad Gita talks about two distinct entities - Aksharbrahman and Purushottam Parabrahman. Purushottam is superior to Aksharbrahman.
My question is, other Vedanta schools do not propagate the idea of two distinct Brahmans. So how they explain these three verses?
Akshar-Purushottam Darshan: an Introduction by Mahamahopadhyay Sadhu Bhadreshdash (translated by Sadhu Dharmasetudas and Sadhu Sushilmunidas)