And by 'a number', I mean a grammatical number. Not a new integer or uniquely weird algebraic entity in some odd field or algebra.
So, let's consider the paucal. This is of course a familiar number, I bet, to most readers. A plural of few. We can consider some potential twists to spice this number up! I doubt combining too many of these in one language works, but potentially some of them may combine. If other numbers also take up some of the
1. Using it with comparatives or superlatives.
In a language with plurals and paucals, and also comparatives and superlatives, comparing sizes of finite sets becomes trivial: comparative on a noun in the paucal means 'fewer', comparative on a noun in the plural means 'more'. The superlative can of course extend this in trivial ways.
2. Using it to signify 'too few'
One could imagine using a marker that derives, say adverbs or maybe a case marker such as instrumental (or just any case), to signify 'too few'. This could of course also extend to 'too little', and produce a situation where mass nouns only have singular forms and an instrumental paucal.
3. 'one out of', 'a few out of'
One could imagine a situation where partial inclusion of the referent (man, am I trying to sound technical?) is always done by use of the paucal. Here, one could imagine that e.g. the case system or the congruence system intentionally 'breaks' a bit whenever this happens. Since there's so many potential scenarios in my mind right now, I will need to describe them a bit.
We shall call this the 'paucal partitive'.
3.1 Northern Eurasian-style case systems
We could imagine that the paucal partitive is restricted only to some syntactical roles. Let's say objects and subjects.
We could imagine that the paucal noun is exceptionally in the genitive for subject and object (or some other non-canonical subject or object cases). We could also imagine that the congruence on the verb has a number mismatch.
3.2 Noun Class Congruence systems
We could imagine that the congruence for the partitive paucal is reset to some inanimate/default type, or potentially to the singular of the relevant noun-class. This might apply even if we're referring to more than one member of the group.
Conversely, we could imagine paucal congruence on a verb with plural marking on the noun phrase? In this case, the construction would conserve noun class but not number. We can, however, imagine that this particular structure would demand that the NP and the verb congruence only differ by one step in the hierarchy plural > paucal > singular.
3.3 Other discongruences:
We can imagine that numerals, adjectives, articles, etc are discongruent in number, case or animacy, and even gender.
We could imagine that the paucal partitive construction also is considered syntactically non-canonical, and sufficiently so as to alter the transitivity of the verb, leading to the use of valency-reducing morphology on the verb, even if the syntactical situation is conserved (e.g. the paucal partitive subject still is the subject, and the object is still the object, despite a passive marker having been introduced on the verb).
3.4. Alignment change
We could imagine that the use of the genitive paucal for partitive paucal subjects could trigger a change in alignment. This use could also well use some kind of infinitive (participle or verb-noun or whathaveyou), and there you go - split ergativity. Split ergativity with objects seems less likely, but could maybe arise from the use of the same participle or verb-noun after the paucal partitive use of the participle has been well-enough established, then extending to the nominative paucal as object of the participle.