I've seen multiple language books, videos, etc. refer to this great, wonderful, magnificent general-purpose counter known as つ. The problem? I've also seen multiple source say that つ doesn't work with numbers greater than 10. Which means I can't personally take this very seriously, and unfortunately, language manuals tend to just skip over any explanation of what you're supposed to do with numbers greater than 10.
Maybe they just mean that you have to change over from the ひとつ、ふたつ、みっつ counting system to the いち、に、さん counting system, but if that's so, there's no way to tell from the way that language manuals tend to word this. So what do you do for general-purpose counting after 10 (or before 1)?