I wonder whether there are rules or guidelines regarding plural nouns in nominal compounds. For example a compound university students list. If there are many lists and many universities is it grammatically correct to say universities students lists? Must all elements be in the plural form or can some be left in singular, even though the meaning is plural? I've seen an expression universities student lists; is it correct?
There is a cross-linguistic principle that words incorporated into compounds tend to lose any inflections (I remember an article in Language in the 80's - probably, from the index, one of the articles in Vol 62 No 1, but I haven't a copy to hand).
So in English, the norm is that nouns incorporated into compounds do not take a plural ending. Where they do, this is usually because the singular form would be ambiguous, often because there is a homophonous adjective. An example I recall is "solid modelling" - the company I worked for in the 80's used this phrase (in the UK, hence the spelling of "modelling"), but other vendors preferred "solids modeling", presumably because they thought that "solid modelling" might be a solid kind of modelling, as opposed to the modelling of solids.
As a general rule of thumb, you want to have just one plural word in such a phrase. The other nouns in the phrase act as modifiers to the pluralized noun and are not, therefore, pluralized. So "university student lists" would indicate a number of lists made up of students at universities. The normal inference would be that there were multiple universities, and it would take some modification to restrict it to lists of students at a single university, or that each list was composed of students at a single university. "A university's student lists", or "each university's student lists", would supply those restrictions.
The expression "Universities' student lists" would correctly mean the student lists of a number of universities, but you would want the apostrophe in there.
I think it is easier to read this with 'student' rather than 'students' as it removes possible ambiguity, creating a noun from the phrase 'student lists.'