Excellent philosophical question!
As Conifold has stated, there is no limit to logical reference from a theoretical standpoint, but there is from a practical one.
While you are using identical subordinate clauses, one could also use varied prepositional phrases in a sentence:
- There is the boy in the house.
- There is the boy in the house on the sofa.
- There is the boy in the house on the sofa of the owner.
- There is the boy in the house on the sofa of the owner with the name Bill.
Do the sentences ever become meaningless? No. Remember, just because you don't comprehend the proof of the Laplace Transform doesn't make the proof meaningless. This is a lesson lost on poor critical thinkers who aren't aware of the Dunning-Kruger Effect. : ) Do they become incomprehensible, yes. And since they do, we just split them up into comprehensible pieces. So, we can rewrite 4 as follows:
There is the boy in the house on the sofa. He's sitting on the sofa which is owned by Bill.
One could also use mathematical operations to differentiate between meaning and comprehension. Consider that 1 can be added to itself, and we can write 1+1, 1+1+1, ..., 1+1+1+...+ 1. Would anyone ever claim that there is a logical limit to how many times we can add? No, but we can make the sentence more comprehensible:
Σ1 from terms 1 to n.
This helps to show a fundamental difference between syntax and semantics. The ability to process syntax to lead to semantics is what both the calculator and the brain do. Thus, as long as one follows the rules of syntax, one can have a meaningful, but incomprehensible sentence. In computation, the study is called formal language. In natural language, the study of such a topic falls under psycholinguistics under headers such as chunking.
And for the record, if you're interested in such topics, you can approach these sorts of philosophical thoughts in the philosophy of language. John Searle in his Speech Acts recognizes distinctions among linguistics which studies specific languages and their features, linguistic philosophy which is an approach to doing philosophy by examining the nature of the language, and the philosophy of language which he describes as "the attempt to give philosophically illuminating descriptions of certain general features of language, such as reference, truth, meaning, and necessity[.]" (pg. 4).