The term in linguistics for a category of 3 or 4 things is "paucal". Most languages with a paucal separate 2 from 3 or 4, resulting in four noun categories/forms by number: singular (1), dual (2), paucal (3 - 4? a few?) and plural (5+). That's quite a common pattern among the world's languages. Polish and the other Slavic languages with this feature are a little unusual in not having the separate dual. A few languages have a trial (3) as a distinct category but it's rare. And some languages distinguish between a greater and lesser paucal, roughly "a few" vs "many", usually with the singular, dual and plural as well, having 5 categories of noun number.

Languages with these features often have lots of irregularities around them, too. In the same way that "pants" are plural for no reason in English, eyes might be plural instead of the obvious-seeming dual, etc. And if that seems all a bit unnecessarily numerical, you may be right; Chinese has gotten by for thousands of years without any plurals at all.