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Śrî Caitanya-caritāmṛta
sarve nityāḥ śāśvatāś ca dehās tasya parātmanaḥ hānopādāna-rahitā naiva prakṛtijāḥ kvacit
“All the varied expansions of the Personality of Godhead are transcendental and eternal, and all of them repeatedly descend to all the different universes of the material creation. Their bodies, composed of eternity, bliss and knowledge, are everlasting; there is no chance of their decaying, for they are not creations of the material world. Their forms are concentrated spiritual existence, always complete with all spiritual qualities and devoid of material contamination.”
Confirming these statements, the  Nārada-pañcarātra  asserts:
maṇir yathā vibhāgena nīla-pītādibhir yutaḥ rūpa-bhedam avāpnoti dhyāna-bhedāt tathācyutaḥ
“The infallible Personality of Godhead can manifest His body in different ways according to different modes of worship, just as the  vaidurya  gem can manifest itself in various colors, such as blue and yellow.” Each incarnation is distinct from all the others. This is possible by the Lord’s inconceivable potency, by which He can simultaneously represent Himself as one, as various partial forms and as the origin of these partial forms. Nothing is impossible for His inconceivable potencies.
Kṛṣṇa is one without a second, but He manifests Himself in different bodies, as stated by Nārada in the Tenth Canto of  Śrīmad-Bhāgavatam :
citraṁ bataitad ekena vapuṣā yugapat pṛthak gṛheṣu dvy-aṣṭa-sāhasraṁ striya eka udāvahat
“It is wonderful indeed that one Kṛṣṇa has simultaneously become different Kṛṣṇas in 16,000 palaces to accept 16,000 queens as His wives.” ( Bhāg.  10.69.2) The  Padma Purāṇa  also explains:
sa devo bahudhā bhūtvā nirguṇaḥ puruṣottamaḥ ekībhūya punaḥ śete nirdoṣo harir ādikṛt
“The same Personality of Godhead, Puruṣottama, the original person, who is always devoid of material qualities and contamination, can exhibit Himself in various forms and at the same time lie down in one form.”