Mahāpuruṣa: I'm not sure if I understand yet. Lord Caitanya Mahāprabhu is svayaṁ bhagavān.
Prabhupāda: Yes.
Mahāpuruṣa: And the appearances of Kṛṣṇa in all the other yugas is also called svayaṁ bhagavān?
Prabhupāda: No. Ete cāṁśa-kalāḥ puṁsaḥ kṛṣṇas tu bhagavān svayam (SB 1.3.28). The list of different incarnations in different ages, they are enlisted in the Śrīmad-Bhāgavatam and it is summarized in the last verse, ete. Ete means "all these." Ete ca aṁśa-kalāḥ. Aṁśa means "plenary partial expansion." Kalā, "expansion of the expansion." There are many expansions directly from Kṛṣṇa and there are many expansions who are expansions from the expansions. So direct expansion is called aṁśa, and expansion of the expansion is called kalā.
Just like Mahā-Viṣṇu. Mahā-Viṣṇu is expansion of the expansion. The direct expansion is Baladeva. The next expansion is Saṅkarṣaṇa. The next expansion is the catur-vyūha. In this way, Viṣṇu, Mahā-Viṣṇu, is expansion of the expansion, kalā. Yasyaika-niśvasita-kālam athāvalambya jīvanti loma-vilajā jagad-aṇḍa-nāthāḥ (Bs. 5.48). Yasya kalā-viśeṣaḥ. Kalā means expansion of the expansion. That Mahā-Viṣṇu is kalā of Kṛṣṇa. Govindam ādi-puruṣaṁ tam ahaṁ bhajāmi **.
So not necessarily all appearances of Kṛṣṇa is direct or He, Himself. There are expansions and expansion of the expansion. That is clearly explained. Ete ca aṁśa-kalāḥ. Some of them are direct, some of them are indirect. But this word Kṛṣṇa is, kṛṣṇas tu, He is but the Supreme Person. Bhagavān svayam, the Supreme Personality of Godhead.