Detail #100: Some ideas about counters

Counters are fairly interesting words. If you're not familiar with them, they function a bit like 'heads of' or 'pieces of' work in English NPs along the lines of the following sample:

• five head of cattle
• six pieces of metal
• ten grains of sand

Languages that use such words more often - and where they are semantically more bleached than in the English examples above - sometimes are described as having only mass nouns. Such descriptions may exaggerate what is going on, but I will not get into that right now.

Obviously, counters enable some neat shenanigans with regards to noun-class-like things.
However, I started thinking about other things these words could be used. The prototypical use is basically along the line presented above - whenever the noun phrase has a quantifier, it needs a counter.

A few ideas that probably don't go all that well together:

• predicative amounts: five CNT house = five house(s), house five CNT = there are five houses
• plural existential statements: solution CNT = there are solutions. The singular would be done by some construction that is invariant with regards to noun class.
• distinguishing indefinite determiners - some distinction like some vs. any marked simply by having a counter or not having one.
• separate counters for specific or estimated amounts. 
• distinguishing communal possession from separate possession - both with predicative possession and attributive possession. (i.e. 'the family's houses (owned communally)' vs. 'the houses of the family members')
• individuating plural actors who would normally be assumed to be acting in consort with regards to certain verbs (CNT we go there' - we go there, each by our own path/manner/etc. CNT the family eat = the members of the family all get some nutrition in whatever way, vs. the family eat = the family eats a meal together.