Gaudiya vaishnavas consider Krishna to be superior than Brahman. It is believed so based on Bhagavad geeta.
There are two verses (I found only two, there could be other verses) in which Krishna said He is beyond Brahman.
- brahmaṇo hi pratiṣṭhāham amṛtasyāvyayasya ca
śāśvatasya ca dharmasya sukhasyaikāntikasya ca
Meaning: And I am the basis of the impersonal Brahman, which is immortal, imperishable and eternal and is the constitutional position of ultimate happiness. (Bg-14.27)
In the above verse Krishna said He is the basis of impersonal brahman.
From the room conversation with Prabhupada,
Ashok Chugani: Swāmījī, may I ask one question which I had much discussion with your śiṣya here. Brahman, the sort of, what we in Hindu philosophy consider as the ultimate Godhead...
Ashok Chugani: Brahman you consider Kṛṣṇa. But He is, of course... He was incarnate. He was one of the avatāras.
Prabhupāda: That is your opinion. [laughter] That is not...
Ashok Chugani: That is our point which I want to clarify.
Prabhupāda: You have to take the śāstra, authority.
Ashok Chugani: Does not Gītā say...
Prabhupāda: Brahmaṇo aham pratiṣṭhā. Read Bhagavad-gītā. You have read Bhagavad-gītā?
Ashok Chugani: Yes, I...
Prabhupāda: Did you not read this?
Ashok Chugani: Well, that's what I want to clarify.
Prabhupāda: [to devotee:] Find out this.
Prabhupāda: Read that.
Ashok Chugani: I am... This, even on the Eighth Chapter you will find.
Prabhupāda: Yes. Brahmaṇo 'haṁ pratiṣṭhā. Read. Just here.
Girirāja: brahmaṇo hi pratiṣṭhāham
śāśvatasya ca dharmasya
Prabhupāda: So He is the pratiṣṭhā. Just like in this room there is illumination. The illumination is spread all over the room. [Hindi---"Please hear"] So the illumination is important or the light is important? What is important?
Ashok Chugani: The original light, source of the light. So isn't Brahman the source of the light?
Prabhupāda: No, first of all try to understand. If the... Just like the sunshine. The sunshine is important or the sun is important?
Ashok Chugani: The original sun.
Prabhupāda: Yes. Similarly, this impersonal Brahman illumination, or effulgence, that is the bodily rays of Kṛṣṇa. Yasya prabhā prabhavato jagad-aṇḍa-koṭi [Bs. 5.40]. So ultimately Kṛṣṇa is important, not this impersonal Brahman illumination. Brahmeti paramātmeti bhagavān iti sabdyate [SB 1.2.11]. You see practical example and learn here in the śāstra, you'll understand Kṛṣṇa is the origin. Ahaṁ sarvasya prabhavo [Bg. 10.8], personally says. Mattaḥ sarvaṁ pravartate. So Brahman also pravartate. But if you don't believe Kṛṣṇa and śāstra, that is a different thing. Then you cannot be convinced. Śāstra-cakṣuṣāt. Your eyes should be through the śāstra, not by manufacturing ideas. So śāstras says this:
yasya prabhā prabhavato jagad-aṇḍa-koṭi-
tad brahma niṣkalam anantam aśeṣa-bhūtaṁ
govindam ādi-puruṣaṁ tam ahaṁ bhajāmi
This is śāstra, Brahma-saṁhitā, that "This brahma-jyotir is the bodily rays of Kṛṣṇa, Govinda." So the rays of Govinda is not so important as Govinda is important. Govindam ādi-puruṣaṁ tam ahaṁ bhajāmi. And Govinda personally says, ahaṁ sarvasya... Sarvasya means everything, including Brahman.
Ashok Chugani: [mis-hears what Prabhupāda is saying as Brahmā] Brahman. With all due respect, I was talking of Brahman.
Prabhupāda: I am speaking of Brahman. Brahman means..., Brahman means this brahma-jyotir. You mean that. Yes, I am speaking that. This brahma-jyotir...
Ashok Chugani: Īśvara is different from Brahman?
Prabhupāda: Īśvara everyone. But īśvara-parama is Kṛṣṇa.
The second verse is,
- yasmāt kṣaram atīto ’ham
akṣarād api cottamaḥ
ato ’smi loke vede ca
Meaning: Because I am transcendental, beyond both the fallible and the infallible, and because I am the greatest, I am celebrated both in the world and in the Vedas as that Supreme Person. (BG-15.18)
Commentary by Baladeva Vidya Bhushana, a gaudiya vaishnavacharya,
Explaining the name purusottama, the Lord speaks of His own true nature. Uttama here means most excellent. Loke here refers to the scriptures written by men. Loka means that whoch reveals the meaning of the vedas. He is praised (in the loke) and the vedas. In the vedas it is said:
The atma, the object of mercy, raising from its body, attains the supreme light, the supreme person and manifests his natural form. chandogya upanishad 8.12.3
That supreme light attained by mercy is the Paramatma. In the scriptures written by men, he is also praised as the supreme person.
So, Krishna is beyond the liberated souls or infallibles which is referred as "brahman" by advaita.