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I have only seen か(個/カ/ヶ) in か月、か年（五か年計画）、か国（六か国会議）、か所、か条.

Is it a productive component which can be used in making other new measure
words?
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2023-07-17T19:37:40.047
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question
grammar suffixes numbers
Is か(個)/ヶ a productive component in measure words (助数詞)?
No, it’s not. You cannot coin a new counter like this.

**EDIT:** か月, か国 and か所 work as ordinary counters in contemporary Japanese,
but others usually appear in historical terms (e.g.
[五箇伝](https://ja.wikipedia.org/wiki/%E4%BA%94%E7%AE%87%E4%BC%9D)) or fixed
phrases (e.g.,
[三が日](https://ja.wikipedia.org/wiki/%E6%AD%A3%E6%9C%88%E4%B8%89%E3%81%8C%E6%97%A5)).
If you are working on historical fiction or fantasy works, you might use this
pattern to create a new archaic-sounding term for use within the work. For
example, something like 三箇龍玉 or 三ヶ龍玉 (Trinity Dragon Orbs) seems reasonable to
me as a keyword in a fantasy work, even though Google does not know a single
example of this. Still, this is a very rare convention, and I doubt this would
be considered "productive" in the linguistic sense.
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If such a mechanism were to exist, then it would be something like:

３カ国語 -> ３カ(の)国語

We understand the hypothesis, but it turns out to be false because we can't
create new counters (we can't go the other way around).

三個の青あざ -> 三個青あざ (X)

Because NUMBER個青あざ should be a noun, but of course it isn't.

So the questions shifted from "how to make counters" to "how to make compound
nouns". They just work conventionally and are spontaneously created as any
many other words.

The NUMBERか[月/年/etc] counter tends to be only used as nouns and not as
adverbs. So omitting our hypothetical の would mean that we didn't need that
function in the first time.

I mean this:

猫の三匹 (as a noun) ＆ 猫が三匹いる (as an adverb)

We can't say: 五ヶ[月/年/etc]+VERB

They are sort of a different breed.
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answer