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Teachings of Lord Chaitanya
The conclusion is that the Supreme Original Personality of Godhead is Krishna—He is called  Leela  Purushottam, and He is principally in Vrindaban as the Son of Nanda. It is also learned from the  Hayasirsha Pancharacha  that nine forms are protecting two  Puris , known as the Mathura Puri and the Dwarka Puri: the four Forms of Vasudeva, Samkarshan, Pradyumna, and Aniruddha, and besides these four Forms, there are Narayan Forms, Nrishingha Forms, Hayagriva Forms, Varaha Forms and Brahma. The above descriptions are different manifestations of the  Prakasa  and  Vilasa  Forms of Lord Krishna.
Now Lord Chaitanya informs Sanatan Goswami that there are different Forms of the  Svamsa  also:  Svamsa  Forms are divided into the Samkarshan division and the incarnation division. From the Samkarshan division come the three Purusha Avatars: the Karanodakshayee Vishnu, Garbhodakshayee Vishnu and Kshirodakshayee Vishnu. The other division is called  Leela  avatars, such as the Lord's incarnation as a Fish, as a Tortoise, etc.
There are six kinds of incarnations: 1. the  Purusha  Avatar incarnations, 2. the  Leela  Avatar incarnation, 3. the  Guna  Avatar, 4. the  Manu  Avatar, 5. the  Yuga  Avatar, and 6. the  Saktavesh  Avatar. Out of six kinds of Vilasa manifestations of Krishna there are two divisions based on His age. They are called Balya and Pauganda. The original Form of Krishna as the Son of Nanda enjoys in two Forms of childhood, namely  Balya  and  Pauganda .
The conclusion is that there is no end to the expansions and incarnations of Krishna. Here Lord Chaitanya describes some of them to Sanatan just to give him an idea of how the Lord is expanding and how He is enjoying. This is confirmed in the  Srimad Bhagwatam , in the First Canto, Third Chapter. It is said there that there is no limit to the emanations of incarnations of the Supreme Lord, just as there is no limit to the waves of the ocean.
Krishna's first incarnation is as the three Purusa Avatars, namely the Maha Vishnu (or Karanodakshayee) Avatar, Garbhodakshayee Avatar and Kshirodakshayee Avatar. This is confirmed in the  Sasvata ,  Tantra .
Krishna's energies are also divisible into three: His energy of thinking, His energy of feeling, and His energy of acting. In His energy of thinking He is the Supreme Lord, in His energy of feeling He is Lord Vasudeva, and in His energy of acting He is Samkarshan Valaram. Without thinking, feeling, and acting there could be no possibility of the Creation. Although there is no creation of the Spiritual World, yet there is the creation of this material world. But both the Spiritual World and the material world are manifestations of the energy of acting—in the Form of Samkarshan and Valaram—of Krishna.