In Gaudiya Vaishnavism, the distinction is made between Kāraṇodakaśāyī Viṣnu (Mahaviṣnu), Garbhodakaśāyī Viṣṇu and Kṣīrodakaśāyī Viṣnu on a cosmological level as the Paramātmā for the metacosm, the Paramātmā for an individual brahmāṇḍa (universe) and the Paramātmā who is immanent within all living beings, respectively. Furthermore it is believed that the aforementioned forms are expensions of the Chatur-vyūha - the fourfold manifestation of Bhagavan in Vaikuntha, being expensions Saṅkarṣaṇa, Pradyumna and Aniruddha, in that order. Is this understanding in line with Sri Vaishnava theology?
In the SriVaishnava tradition, as user Surya Kanta Bose mentioned, we do not recognise the forms Kāraṇodakaśāyī Viṣṇu, Garbhodakaśāyī Viṣṇu, and Kṣīrodakaśāyī Viṣṇu.
Instead, we have five categories of forms of the Lord, which are Para, Vyūha, Vibhava, Arca and Antaryamin.
Para refers to the supreme form of the Lord Sriman Nārāyaṇa in Paramapadam (SriVaikuntam).
Vyūha refers to the fourfold manifestation of the Lord as Vyūha Vāsudeva, Vyūha Saṅkarṣaṇa, Vyūha Pradyumna and Vyūha Aniruddha.
Vibhava refers to the different Avatāras of the Lord such as Rāma, Kṛṣṇa, and Nṛsiṁha
Arca refers to the forms of the Lord enshrined in temples such as the images of the Lord in the Divya Desams and other holy sites.
Antaryāmin refers to the form of the Lord as the Supersoul, swayed within the heart of all creatures.
Kṣīrodakaśāyī Viṣṇu who is the Supersoul of all beings in the Gaudiya Tradition can be compared to Antaryāmin, the Supersoul of all beings in the SriVaishnava Traditon. But there is no form in SriVaishnavaism which can be compared to the other two-Kāraṇodakaśāyī Viṣṇu and Garbhodakaśāyī Viṣṇu.