Are there any languages where there are different plural forms depending on the count?
10 cooks (this would be a different word)
Linguistics Stack Exchange is a question and answer site for professional linguists and others with an interest in linguistic research and theory. It only takes a minute to sign up.Sign up to join this community
The most common form of this involves having a dual number, used for exactly two things, and a plural number, used for any more than that. You'll find this in older Indo-European languages and modern Inuit and Semitic languages.
Some languages also have a trial number, used for three things; the trial only exists in languages that also have a dual, and has never been documented to exist in nouns, only in pronouns.
Others, instead of dual/plural, have a paucal/plural distinction. The paucal is used for "a few" of something, that is, any small number. I'm less familiar with this one, but something similar does exist in Russian, only in the genitive case:
According to the "Grammatical number" Wikipedia article, there are languages with dual and trial numbers, as well as forms that contrast small numbers with big numbers. The article contains a... number of examples.
To talk about what I know, Proto-Indo-European is assumed to have dual inflections, as many of its daugther languages did, and some still do. So, at least a dual number isn't particularly uncommon among languages that have grammatical number in the first place.
This may be a partial answer because I don't remember details, sorry for that.
A Russian noun can have up to 4 numeral endings (including the singular forms). The first is its "original form" and is used only for 1. The second form is used for 2, 3 and 4. The third form is used for 5 to 10. These three forms also apply to (21, 31, 41...) / (22, 23, 33, 44...) / (25, 36, 47, 58, 69 ...). A fourth form exists for 11 to 19.
I have also heard that something similar exists in Polish, but I know nothing about that.