Chiming in from theoretical linguistics: it is impossible for natural languages to "count", i.e. make reference to numbers other than 0, 1 or infinity.
As an example, there are languages where prenominal genitives are impossible (0).
Then, there are languages, such as German, where only one prenominal genitive is possible (1):
> Annas Haus
> *Annas Hunds Haus
Finally, there are languages, such as English, where an infinite number of prenominal genitives are possible (infinity).
> Anna's house
> Anna's dog's house
> Anna's mother's dog's house
> Anna's mother's sister's ... dog's house
But there are no languages where only two or three prenominal genitives are possible.
This property is taken to be part of Universal Grammar, i.e. the genetic/biological/mental system that makes human language possible.
As a German speaker, the claim "more than one prenominal genitive is impossible" seems interesting but perhaps not entirely accurate. As a non-linguist I probably misunderstand the meaning of prenominal genitive and might be missing your argument's point. For the overarching discussion we should note though the great variety of refering to "more than one element" in German.
> Anna's mother's sister's dog's house
> Das Haus des Hundes der Schwester der Mutter von Anna.
It's difficult to parse though. We only get to know about Anna at the end of the sentence. Consequently, we avoid such sentences or use workarounds.
> Von Annas Mutters Schwester dem Hund sein Haus.
If you ever use such a construction German speakers will correct your bad language but they will perfectly understand the sentence's meaning.
As an example, there are languages where prenominal genitives are impossible (0).
Then, there are languages, such as German, where only one prenominal genitive is possible (1):
> Annas Haus
> *Annas Hunds Haus
Finally, there are languages, such as English, where an infinite number of prenominal genitives are possible (infinity).
> Anna's house
> Anna's dog's house
> Anna's mother's dog's house
> Anna's mother's sister's ... dog's house
But there are no languages where only two or three prenominal genitives are possible.
This property is taken to be part of Universal Grammar, i.e. the genetic/biological/mental system that makes human language possible.