Using "quite" with a noun
They were quite champions today.
That version is not used but perhaps not for the reason you think.
Let us start with the singular.
He was quite a champion today.
That is possible but not the usual idiom. We are more likely to say:
He was quite the champion today."
I have no idea why.
Pluralise that and you get:
They were quite the champions today.
...and that is idiomatic.
P.S. I see that this is currently being discussed in the comments. When we say "'You are quite the champion" it actually means "You are are quite a champion." Again, I don't know why. Maybe someone else has an explanation.
P.P.S.
We should not be led astray by the fact that the word happens to be 'champion'. You could perhaps object by saying, "Well there can be only one champion". In fact the idiom works regardless.
Example:
He came from an upper middle class background somewhat similar to myself however, his father was quite the masked jackal and some of those traits would manifest when I would converse with him on different topics.
Opvs Daemonvm: The Devil's Diaries By Draconis Blackthorne
Quite technically cannot be used in front of a plural noun and still be grammatically correct. Using the instead of a/an when adding quite in front of a plural noun is really an idiomatic expression showing uniqueness. ex. She is quite the singer or They are quite the group of boys
As @Jim added above, quite the champions would be usable, but when looked at from a grammatical standpoint, it doesn't mean what you are trying to get across.
In conclusion, 'quite' can be used to describe singular nouns, but cannot be used in the same way to describe plural nouns.
'Quite' can't be used without a determiner in these constructions.
Although constructions like 'Those were quite some days!' cannot be labelled ungrammatical, the exact construction used affects acceptability or at least idiomaticity. Thus
'Those were quite some guys!'
sounds better than
'They're quite some teachers!' or
'They're quite some champions!'
ODO only gives examples of constructions using 'quite some' in its two senses (quantifier and emphasiser) followed by a singular noun:
Definition of quite some in English:
1 A considerable amount of: she hasn’t been seen for quite some time
2 informal way of saying quite a —— . Old Darlington was quite some place to live in.
............
I'd just use the plural form some, without the additional emphasiser quite:
They were some champions today.
AHDEL says that this usage is informal:
some adj.
- Informal Remarkable: She is some skier.
Collins does not add this caveat, but (wrongly) restricts the usage to a singular noun:
some determiner
- (usually stressed) an impressive or remarkable: that was some game!.